If so, then no, using randomness to disrupt search only resets the search to continue at a different (random) spot in the global search space. That kind of approach certainly can escape local minima, but it doesn't diminish the amount of total time/effort required to do (non-convex) global search.
I think the long history of our attempting to use randomness to improve search has shown that all naive approaches inevitably fail unless the number of processors available can be scaled up to 'equal' the number of decisions required to explore the entire search space (as quantum computing seeks to do). But maybe the formal resolution of that question will come only after we prove P != NP.
The lottery tickets are random but they are basically - as I understand - smaller graphs that have the same strength as a larger graph.