Maybe not, because (a) each union can still aggregate the interests of hundreds or thousands of workers and (b) it's much easier for a few unions to collaborate with each other than for hundreds or thousands of individual workers to do so.

This depends, of course, on how exactly the new unions are allowed to form. It seems unlikely that the NLRB would implement policy in a way that allows dozens of unions, each with a handful of workers; but I guess if that happened, it would end up just like what you're saying.