If they have had a valid Orthodox conversion, will they be accepted and integrated into a Chassidic community if they want and be able to marry into it? I know this communities are very close knit. (I'm looking into converting to Judaism)
Definitely! There are many Chassidic Jews who are giorim. Although some communities are not so open to with the marriage issue. Gerrer chassidim for instance are not so accepting. I have an aunt who became religious and their child had a hard time getting married. But he did. It really depends. Chabad Lubavitch, on the other hand, is pretty open. But in the long one we are all Jews, and whatever choice you make if you end up converting is fine. The only thing is you really have to make sure it is a Rabbi who is really orthodox and is really authenticated.
P.S. any conversion by someone other than ultra orthodox is not valid. That's because it is not something to take lightly or to dunk in a regular swimming pool with. Conversion is very serious and needs to be strict and anyone who is not orthodox doesn't care so much about Jewish law and are more lax
Now, Chasids for the most part are open to anyone sincerely converting into Chassidic Judaism. But, the conversion would have to be good enough for them. For example, most Orthodox would not accept a Conservative conversion, but some might. However, all Chassidic groups will not accept anything other than an Orthodox one. Still, some Orthodox conversions might not be good enough for some Chassidic sects. A modern Orthodox conversion will earn you Jewish status with most, but there are still some which will require you to go though an additional process to fully convert to their sect. But, with the exclusion of one Syrian sect that I have heard about, there shouldn't be any obstacles in your way if you truly want to convert.