Kind of yes, kind of no, sometimes.
Putting a competitive slant on the training would very likely make development faster.
But, it would also very likely restrict the variation of application.
This is the bit that could be good or bad...
Any competition really requires a ruleset - competition implies trying to win, so you need a framework to judge what constitutes a win.
As an example, people who train toward Olympic style tkd competition get very good at trying to win under those rules - but are those rules necessarily good for developing "street" application?
Someone in a tkd school with that sort of training would probably be better at that faster than me, because that's different to my training - but outside those rules, would they necessarily be able to do anything if I punched toward their head, or clinched them, or swept them?