In principle, yes, for sure, we could detect it. For example, it would still generate gravity and be uniquely identifiable this way. But then, superluminal matter breaks causality, allows sending signals back in time and, to the best of our knowledge, is unphysical.
The superluminal speed is not an infinite speed, it's just faster than the speed of light, of course, but it called "instant". For example, a photon of light is emitted or absorbed "instantly", which is not true, obviously, because it means infinite speed of transition.