To this question I received three different answers. Most responded quite promptly that, no, it could not be false. Several opponents of the consensus then current responded that not only could it be false but also it was false. A very few smiled and asked me to clarify my question. Yes, any scientific theory could be false in the abstract, but given the current state of knowledge, the basic axioms of evolutionary theory are likely to continue to stand up to investigation.
Philosophers tend to object to such conceptual plasticity.
Otherwise, they do not mind it at all. In fact, they get irritated when some pedant points it out. Most scientists are not philosophically inclined and will make use of whatever is a help in their work, but not in the way Feyerabend thought. Reflective scientists know that it's all how you ask the question that counts. Most physicists would not immediately think that atomic theory could be false, either.