The short answer
No. Evolution could not have occurred if the laws of nature were not fairly stable at least since the time evolution began. Beyond that, neither evolution nor creationism entails anything about whether the laws of nature change over time.
The longer answer
I. Evolution says nothing about whether the laws of nature are fixed before the first replicator
Since evolution does not take place until replicators exist, evolution cannot entail anything about the stability or variability of the laws of nature before the origin of the first ancestral replicator.1
II. Evolution requires the laws of nature to be approximately stable after the first replicator
After the first ancestral replicator arose, evolution would have been able to work only against a backdrop of very stable laws of nature. Had the laws of nature changed dramatically sometime later, that change probably would have wiped out all life.
III. Young-earth creationists claim that the laws of nature were different in the past
Michael Ruse notes that the young-earth creationists who typically make this claim contradict themselves: they elsewhere argue that the natural laws governing the rates of radioactive decay and sedimentation were different in the past, since this is the only way they can save their beliefs from falsification by multiple convergent lines of evidence (Ruse 1982:305). Some creationists likewise argue that the speed of light was different in the past, or that the second law of thermodynamics was not in effect until God cursed all of creation in a fit of childish rage at Adam and Eve.
IV. Creationists would be unlikely to give up creationism if it were discovered that the laws of nature are not fixed
Some legitimate scientists do think that the laws of nature may have changed very slightly over time. If this were proved that this was the case, do you think creationists would take this to confirm evolution and falsify creationism? Of course not. Were it ever conclusively demonstrated that the laws of nature had changed, one can be sure that creationists would suddenly turn around and say that this is precisely what creationism predicts, and precisely the opposite of what evolutionary theory predicts. Even then, they would be mistaken: aside from the points made of above, neither evolution nor creationism entails anything about the fixity of the laws of nature.
1 I say “before the origin of the first ancestral replicator” because it is logically consistent with evolution that batches of replicators before the first ancestral one were destroyed by changes in the laws of nature. But once you get to the earliest replicator that is ancestral to us, the laws of nature need to remain approximately fixed at least from then until now.
Ruse M. 1982. Darwinism Defended: A Guide to the Evolution Controversies. London: Addison-Wesley.