To an extent yes, though I'm not particularly beholden to the general term "the Deep State" (hearing new terms for old ideas tends to piss me off) nor this idea of Trump heroically, in some grandiose fashion, fighting against it though that's not to say he is fighting against certain vested interests that is undeniably true.
And that really is all it is. A group of people in media, public elected office, and the bureaucracies possibly with the same political ideology/faction (a usual commonality) collaborating/colluding to advance or protect an interest they have by fair or foul means.
Let's take the media/government connection. In this case you have examples of people from both political spectrums who leave office or a campaign to join say ABC, NBC, etc. (see George Stephanoupolis for example) or who have familial relations with political figures who likely used their influence to get their relatives in positions of media (see Fredo Cuomo). This is absolutely nothing new and not surprising nor limited only to one side though I think, if the Left has their win with a legitimate or illegitimate Biden regime, then it will become a far more exclusive monopoly since I'm sure Fox will be pressured to purge contributors like say Gowdy, but that's beside the point.
The government/bureaucrat connection should need no explanation. Politicians appoint bureaucrats, plain and simple, but some go out of their way to install favorites into juicy positions. Maybe it's Ted Cruz wanting to get some Colonel from Texas he knows into the Department of State or something or Donald Trump appointing Mitch McConnell's wife as Secretary of Commerce if I'm not mistaken as a favor/nod to McConnell I'm sure. This is pretty standard stuff. These people are intended to circle the wagon if necessary or go after somebody the Inner Circle construes as an enemy to them and their interest.
The whole thing pretty much is the contemporary version of I scratch your back, you scratch mine/client-patron relationship. This is why I don't care for the new lingo "Deep State" because it's based on an idea as old as the Romans.