In the ordinary run of things no, but getting under the cap makes it a bit more likely.
Don't get me wrong, Jarry's been good, just probably not quite good enough to displace someone. And if he does, I think it'll be as much about whether he's showing good habits and maturity around camp as anything. Everyone who cares to know knows that Jarry's got a lot of talent and can be as good as DeSmith right now - the question is whether can keep his focus and do that in the uneven rhythm of a back-up.
edit: Also, in a super deflated market for goaltenders, maybe DeSmith might be a little more likely to get a trade return if they want to avoid waivers/conversely a few NHL games might boost Jarry's value if they get DeSmith past waivers but see that as a short term thing. Minor consideration but it's there.