A difficult question to answer, because many elements are not precisely defined. But let's just say for a moment that 'intellect' is conflated with 'universal Turing machine' and 'thinking' with 'processing a program'.
There are of course limits for any finite UTM: on one side, you cannot 'probe' thoughts too deeply because of constraints on memory/energy/time, on the other side there are thoughts that are simply too complex. So no, an AI could never imagine anything that is too complex or too expensive for it to think.
For us humans the situation is even worse, because our brains are no computers, and we are very capable of imagining incoherent things.