Many people in central Bosnia identified as Yugoslavians before the war and I would say most in the same region born in late 60s, 70s would have identified the same. So when someone says Yugoslavia, I think Sarajevo and Bosnia, not Serbia.
So by the end of yugoslavia, got relatively substantial but still by far the majority always identified with some specific ethnicity.
Now I presumed most people revised their identification in 90' for political reasons/safety, but could be emigration as you say played a significant role too, especially in bosnia.
And yeah, a fair proportion would prob be offended by an imputation of yugoslavian identity today, because of the ethnically divided politics.
But I think further than that, a significant chunk of the people not too happy that yugoslavia failed and disintegrated (such as myself and I believe many left-leaning people around) still can't see much sense in identifying as being ethnically yugoslavian. Yugoslavia is no more; yugoslavian identity was a composite one in its rather recent origin; people knew specific ethnicities of their parents and choose to think of themselves as yugoslavian first, or interpreted having parents of different ethnicities as being that identity. As a political project - and it was that - it died just by the time it was getting any substantial traction, so seems rather pointless today.