Can MS Project change the % assignment, when doing resource leveling?

No. Levelling never changes assignments. It produces a feasible solution if one exists, but it is not guaranteed to be optimal.

In this case, whichever combination of leveling options are used, Task2 gets delayed in its entirety, and is scheduled to start after Task1 finishes.

You seem to be trying to get it to give you a solution which is "optimal" or "ideal", being defined (by you) as producing the shortest duration.

However, "optimal" can be defined in various ways depending on what the planning strategy and goals are, and MSP can't read your mind to know what they are.

In this case, it seems at first obvious that MSP should know that A is/becomes available for Task2, but that is only because in this simple case there are only two tasks and one resource.

Although not perfect (because it does not optimise) MSP levelling still works a treat to give you a plan which is at least feasible after you have made one which is not. So that's a good thing, right?

At execution, if A really does become available to start Task2 in the first week (as long as its predecessors are finished), then it will come out in the updating when you find out that Task2 started and finished earlier than scheduled. So the planning is conservative (as it should be) and the execution is aggressive and opportunistic.