Yes, and it not as illogical as it might seem.
The seeming illogical nature of said “un-liftable rock” is the result of your language not the concepts.
Does an all mighty God in the natural course of his existence lift rocks? No that absurd. To create such a situation we would need to add a condition.
Said god would have to inhabit a body or structure to act on such a rock, in this case lift. If God has said body (the body has the limitation of not being able to lift certain weights) that is an example of an expression of God not God(as a whole) and so said “body of god” could not lift the rock well the total being that makes up god could do anything with said rock thus it could be said, god could create a rock his expression could not lift.
well see, your not acting objective. It can certainly be said that there are things God can not do without fundamentally changing us as observers. For example, if God made us all expressions of peace and harmony, we could not act independently of our environments. We would not be us. The world would not be...
So if something exists. God does not do things that contradict that. That does not however mean God can not do things that contradict that, it simply means doing so fundamentally changes the observed and we can conclude He does not do those things, we can even say he can't do those things, but that has an important caveat.