Time? No...I'm reasonably certain. Time arises as an intrinsic component of change-of-state of phenomena. Phenomena are readily observed to change state (even if uncertainty in those observations is inevitable), and state change implies "time" by logical necessity. Without time, "before" and "after" are incoherent concepts. Nothingness has, by definition, no capacity for state change...and thus no time.

Space is trickier...a lot trickier. Simple vacuum is not "nothingness," and that's pretty much a matter of experimentally-determined fact. We don't experience or observe genuine nothingness; for us it's purely conceptual, given that our entire existence is based on "somethingness" (if you'll excuse that linguistic atrocity). In genuine, complete nothingness, are concepts like spatial dimensions have any coherent meaning or applicability? Would it be possible to validly "hold a yardstick up to" (as it were) any form of nothingness? Measurement itself implies something to measure, not nothing. When we mentally apply volume to a mental concept of nothing, is that application even remotely justified?

Matters like this are why I studied (and continue to study) philosophy of science.