I am not sure Ubergeek is right in inferring the Welsh were simply submerged. The original settlers of the north-east corridor were British, Germans, Scots-Irish (meaning Scots coming out via Ulster) and the Dutch Padroons. If the Scots managed to stay on the surface, why not the Welsh?
Presumably some Welsh came out with the British. The point not mentioned so far is religion. All the above, and the Welsh, were presbyterian. The country that became the USA in 1780 was a protestant country. So the Welsh would have been homogenous with the others.
Nothing changed until 1830, when the first mass Irish immigration started (there was a potato famine in Ireland, not THE potato famine, another one) and this was a real change as they were catholic. There were anti-catholic riots in Boston in 1836 because there were so many immigrants.
However many, it was a drop inthe barrel. The US census shows that population growth in the USA came first and foremost from the Americans themselves. The descendants of the Welsh who came to Boston migrated westward to the Great Lakes. The trouble was, by that time they called themselves New Englanders.
Perhaps if the American Revolution had not taken place, all these national groups would have retained their own identity. Just a thought.