I think that's unlikely. What the idiots that keep reporting him don't seem to grasp is that his conduct has to be tied to his practice in order to be actionable. Nick acting like a drunk Internet shitlord is both out of their jurisdiction and (often) protected speech. The idiots reporting him are trying to apply the same tactics they would employ to get somebody fired, but not understanding that a license issued by a government authority is
entirely different.
To put this in better perspective, it would be like somebody here getting their driver's license suspended over saying "nigger." That's not gonna happen. At least not for those of us in the U.S..
@AnOminous also put it best at one point: In reading those complaints, the first thing they'll usually check for is whether the complaint is made by a client. party, or attorney to an action that the lawyer being reported on is involved in. If the answer is no, it'll usually get binned PDQ.
You're right that all of the complaints that spur from random comments said on Nick's show are going to be thrown out without any investigation, but it's worth thinking about the timing of the most recent complaint saga.
At the time Nick read out the complaints, he was pissed. The Keffals brigade had just got his Twitter account banned, and they were about to take out his Youtube and Twitch accounts as well. So not only did he read out the response from the MN Office of Lawyers Professional Responsibility, he also read out the complainant's names and said he'd be posting their addresses on Locals later.
That got put on ice when he got banned from Youtube. My memory may be wrong, but IIRC, when he got restored to Youtube he said he would probably put the addresses up at a later time., and then he disclosed he's being investigated again and we haven't heard anything since. He may have gone too far this time, IMO. You're right that someone being an attorney does not abrogate their First Amendment right to express their opinion. And yes, ethics complaints against attorneys are kept confidential for the benefit of the attorneys, who still have the right to publicize the substance and disposition of those complaints if they want to.
But if Nick is really being investigated again by the OLPR, I suspect what's going on is that they or one of the complainants are alleging that Nick's threat to dox the complainants constitutes intimidation that will deter people from going through the ethics complaint process. The frame of "if you file an ethics complaint against me, I will post your full name and address online to my several thousand braying paying fans" is a
terrible look for an attorney, even if the complaints are frivolous, which they were in this case btw. It may not be a terrible look for an entertainer/shock jock, but it's a
terrible look for an attorney.
This
2000 article by an OLPR lawyer notes that intimidating a potential complainant, even one whose claim is unsubstantiated, poses a risk of creating "a chilling effect on the bringing of complaints, which are of public importance" and therefore may violate Rule 8.4(a) of the Rules of Professional Conduct, which prohibits "conduct that is prejudicial to the administration of justice":

Now the conduct in the cited case was aggravated because in addition to leaving a voice mail in which the attorney asked the complainant to "give [him] a call or come into [his] office because you are going to hear from [him]", he later appeared to threaten a lawsuit even though individuals are immune from civil liability associated with making ethics complaints in Minnesota. And guess what: the initial complaint against this guy was dismissed! Just in 5 minutes of searching I found multiple cases in Minnesota alone where the lawyer gets hit with an ethics complaint and freaks out and threatens to sue, which results in professional discipline even though the initial complaint was later found to be baseless.
The bottom line is that even though the rules may have been written at a time when most people were still in the phone book, the people judging these complaints are not stupid. The stream is there and you can plainly see by his attitude that Nick viewed the dox (and potentially even the threat of dox) as a reprisal against the people who made frivolous complaints against him. Same attitude existed with the Locals post where Nick mocked the guy who prostrated himself and begged for his address to not be made public. Guess what. The complaints were frivolous, but you have to sit there and take it. You can gloat all you like when they're dismissed if you like. Nick could probably argue that he had a legitimate interest in revealing the names since it revealed social media figures who urged complaints against him didn't bother to do so themselves. But what you can't do, at least according to the OLPR, is engage in conduct which is deliberately intended to intimidate potential ethics complainants.
Nick better hope that they don't conclude that his behavior falls under that category. But at the end of the day this was just another example of Nick's poor decision making that is spiraling out of control, and I don't have any sympathy. First, even if this goes anywhere, the most likely result is be a private reprimand where they slap him on the wrist and tell him "don't do this again". But secondly I don't have sympathy because he was dangling the dox as a way to promote his Locals. Even Harry Morris, who has been in the sektur for about 5 minutes, realized that the move is to post somewhere in an anonymous or pseudonymous manner that
cannot be linked directly back to you.
That last comment brings me me to a fun hypothetical scenario that could be embarrassing for Nick.
Let's say there was a person who is accepted to actually have had an attorney-client relationship with Nick.
Let's say that this former client has repeatedly stated that he believes that he has concerns about Nick's professional conduct in the context of that attorney-client relationship, and in fact already mused publicly about filing an ethics complaint.
Let's say that this former client stated for months his desire to keep his home address, which, completely hypothetically, was located in the Los Héroes suburb of Mérida, Yucatán, México, out of public knowledge.
Let's say that this former client - let's give him the name "Ethan Ralph" - could thus make a facially plausible claim to the OLPR that he was intimidated by Nick's actions into refraining from filing an ethics complaint.
That would sure be an interesting and hilarious scenario. Luckily for Nick, this hypothetical individual has two dozen other feuds on his mind before this one, and he lacks the intelligence to competently prosecute even a single feud at any given time.