If I had to imagine anyone sending mercenaries to go after the Courier, it would probably be Mr. House rather than the Mojave Express since the platinum chip is his ace in the hole for the war effort. I believe Mr. House already knew that Benny had the chip by the time you wake up so sending mercs after you would be a waste of time. Sending them after Benny wouldn't work either since Mr. House even explains that he can't get close lest Benny uses the chip as a hostage.
It quite obviously IS Mr. House. He needs that chip, and if you're not going to follow Victor's directions to help him get it, and instead, you're just going to spend weeks or months exploring the Mojave, realistically, he would retaliate, since
he needs that fucking chip, and if you're not going to help him get it, he's obviously going to be pissed, since the Legion and the NCR are gearing up for a final battle, and realistically, neither side is going to wait for some dumb mailman to get to Vegas before they put in place their final plans. Especially the Legion, which already has a plan, and has most things already in place.
In the same vein, once House or Caesar start giving you quests, it also makes no sense that you can put them off for hundreds of hours of gameplay-time (which translates into weeks, or even months of ingame time) while they wait for you to finish your task. Caesar, especially, has an extensive spy network and hit squads all over the Mojave, so taking too long with his quests would realistically end with him getting pissy with you and either sending someone to threaten you or kill you, especially if he finds out that you've just been taking a break and wandering around town instead of say, killing the Mojave BoS, assassinating Kimball, or recruiting the White Gloves or the Boomers for him. Caesar doesn't give the impression of a very patient man, so it's highly unlikely that he'd just let his agent take a vacation after they've been given a task.
But that never happens, since the last time where they did have timed quest in a Bethesda-style open world game, it was a mess. Sure, it adds realism, but gameplay-wise, it is very constricting. So while lore-wise, the note is important, gameplay-wise, it's hot gas, like the Sole Survivor being obsessed about their kid. Sure, he says he wants his kid back, but in the end, it gets in the way of playing an open-world game, just like how timed quests do, so it's just hot gas and nothing else.
May means might. It does not not mean will, must, shall or has.
It still leaves the possibility open. Meanwhile, no one is going after the Sole Survivor if they fail to find their son.
This isn't a legally binding contract simply because there are no courts to legally enforce anything until the Second Battle of Hoover Dam is over.
You haven't been reading the loading screens, have you? Criminals in the Mojave are shot, not tried. There's no courts, just a Judge Dredd-style of enforcing the law by gunpoint, and nothing else. Especially after the Powder Gangers broke free.
so at the time the player is woken up by Doc Mitchell the Courier is not being sought by anyone, even the Mojave Express. Mr House is watching over the Courier and Victor saves the Courier, he doesn't kill him or her.
Victor obviously is trying to get the Courier to confront Benny. If the Courier doesn't do that and faffs around for weeks or months on end, Victor and House would clearly be displeased, and would realistically hold the Courier responsible.
But that never happens, because timed quests in open world games, while realistic, end up being a mess, so gameplay-wise, it ends up being an empty threat.