I'm going to start off with saying absolutely not. As long as you have an instrument that is well set up to your tastes, has electronics that won't detract or sound terrible, it really doesn't matter what you play. I've seen er.....not so good bassists play on incredibly expensive instruments and you know what, they still sound terrible. I've seen great bassists play on mid level, even budget instruments and sound great - I saw Marcus Miller playing one of his Sire basses in concert, and that guy blew the house down with that thing. Not to mention numerous great ones on middle of the road priced instruments, Geddy Lee, James Jamerson, Louis Johnson, an endless list who play on "average" Fender, Musicman basses not the boutique level Sadowsky basses.
That to me is definitive proof that no, a boutique priced bass isn't needed, just a good playing one and these days, even budget priced instruments are so much better than those years ago.
However, if using a boutique bass makes you feel like a better player, is more comfortable, then that's the right bass for you. Whatever makes you enjoy playing the bass but don't try to convince anyone that to be a better player you need to spend a lot of money because that's absolutely not true.