No, they wouldn't. Modest progress in engineering and cultural adaptation, would produce generation ships large enough to sustain a human colony capable of traversing the galaxy on the scale of thousands of years. On the other hand, we could launch a ChatGPT-enabled* probe to arrive at Proxima Centauri in about a century with today's technology.
If you think objectively about it, "physics paradigms far beyond our understanding today" do not necessarily exist. Or if they do, they will not necessarily contribute significantly to our ability to traverse interstellar distances. While it is hubris to assume that we know everything; it is foolhardy to assume that there is gold at the end of the rainbow.
* note that ChatGPT is rather pathetic compared to intelligent life; but it's what we can ship today