Yes, it will be possible unless you specifically construct your definition of consciousness to make it impossible. However, having a mind is unnecessary (and inefficient) for the most intelligent possible machines. Imagine extremely advanced future branches of statistics, which have yet-to-be-invented but still entirely statistical methods for discovering state spaces and causal rules, all with formal proofs of optimality. Imagine that, even if executing these methods is impossible in physical hardware, future computer science is capable of proving optimal sampling methods for a given problem and level of available computing resources. A machine that executes these algorithms is smarter than us, but does not have a mind.
Will we construct machines with minds despite that? Since "to see if we can" is usually sufficient motivation for humans, I expect yes.
Biologically-inspired computing techniques will probably lead to computers with minds, and I can see these computers eventually becoming smarter than humans. Will we make such machines before we invent enough of future-statistics to make a mindless machine that's smarter than us? I don't know, that's an interesting question.
Will we construct machines with minds despite that? Since "to see if we can" is usually sufficient motivation for humans, I expect yes.
Biologically-inspired computing techniques will probably lead to computers with minds, and I can see these computers eventually becoming smarter than humans. Will we make such machines before we invent enough of future-statistics to make a mindless machine that's smarter than us? I don't know, that's an interesting question.