It is in principle falsifiable, I believe, yes. The statement "there is no Strong Emergence" is falsifiable, at least. To falsify it, you could devise an experiment to show that fundamental particles behave in ways that are fundamentally different when they're inside of an actively conscious brain than they do when they're not in one.
If all fundamental particles always behave according to the same principle regardless of whether they're part of a conscious being or not, then that means consciousness is not exerting downward causation in a strongly emergent way, so an experiment of the above variety would sufficiently demonstrate downward causation (imo) and falsify the claim there's no strong emergence.
I don't know about falsifying the statement "there is strong emergence" however.