Based on what I have learned from others with much more knowledge and experience, yes, if you get cuttings from UCD, they will be infected with FMV. It also sounds like cuttings/plants from many other sources are likely to have it as well, and if your plants are "FMV-free" today, they probably won't be for long. The in-ground Brown Turkey I bought many years ago from a local nursery also has FMV, but I never even knew the problem existed until reading about it on F4F. Sure enough, when I examined the BT's leaves closely. I could see the telltale "patchiness" of the green pigment--but it has never caused any problem.
As near as I can tell from what I've been told, and what I've seen in my UCD cuttings, FMV seems to manifest itself periodically in mis-shapen leaves and/or uneven clorophyl distribution, and then the plant reverts back to totally normal-looking growth. It sounds like various things can trigger the symptoms, and it affects different varieties in different ways. Some of my cuttings (Tena, Excel) never showed any signs of FMV, but most of the others have a few weird-looking leaves. The only reason I posted my original question about the Celeste was because it looked so different from the others that I thought it must have had a different problem, and I was actually quite relieved to learn it was probably just FMV. So, my personal opinion is that it's something I accept as part of growing figs, and I'm not going to worry about it.