The drops happen (if implemented) in the same order, but in a different place, half the point of become is to put any needed drops first before the call, as otherwise it's not in tail position and we can't do the optimisation.
So the borrowck can become involved if our become foo(bar, &baz) borrows baz but baz's type impl Drop - the diagnostics aren't great today, but then the feature isn't finished so it's not a priority.