If abstractions are in fact real, not mere shadows, then their existence in the mind as abstractions suffices to demonstrate their reality.  Thus, to conceive of something is to demonstrate the possibility of its existence. 

A problem here, beyond the fact that abstractions are mere shadows, is that it’s never quite clear what it means to conceive of something.  How would the conceiver respond to the simple denial that what he claims to think cannot be thought?  Can the Cartesian truly conceive of himself as a brain in a vat, a disembodied intelligence? What would it mean to be able to do such a thing? what does it look like?  Simply nodding at the sentence, “I am a brain in a vat” does not suffice, nor does suggesting that the thought does not entail an obvious logical contradiction akin to “square circle,”  because to grant this gives away the whole game. 

If we’re Aristotelian embodied souls, then, no, you cannot conceive of yourself as a free-floating intellectual substance.  If we’re Cartesian souls, then we can.  To simply say that it’s possible or impossible is to beg the question, and the contest will inevitable devolve into the question of what you can and cannot truly conceive.  But how can I doubt what you claim to be conceiving?  We cannot ground an argument on such a flimsy foundation.  We must take another tact.

Said differently, the argument is backwards.  We recognize our ability or inability to conceive of something from our actual, particularized, and concrete experience in the world, not by abstracting away from that experience to a tenuous and hypothesized world of thought.