I have a master’s and nearly a PhD in linguistics, and having studied ASL quite a bit when I was learning it to teach my son, I realize that ASL is a completely different language from English, in many different ways. I used quotes around the word “foreign” because from a technical point of view, it is not a foreign language. As Monty points out in his post, there are variations of sign language in different countries, and they are not necessarily at all similar to each other, except in that they use hand gestures, finger spellings, and body/facial expression.
When I was learning ASL for my son, I was also determined NOT to use SEE (Signed Exact English). At the time, we did not know if he would ever hear well enough to speak English, and the grammatical bits of SEE are completely extraneous to a fluent speaker of ASL. If his hearing had not improved, we would have continued with ASL, and done everything we could to help him learn that language well. His grandparents were even willing to learn ASL if necessary.
As it was, he did actually use sign language as his “first” language, and he was as creative in his use of signs as a hearing child might be in his use of spoken language. For example, we made up a sign for Cheerios–his only finger food at the time, and well before he could finger-spell anything that complicated, which was a C-hand moving to an O-hand, kind of like chewing. He learned to associate that sign with eating in general, and used the sign spontaneously to tell us that he was hungry, even though he didn’t want Cheerios specifically. He also used More and Like spontaneously on a regular basis.
As with any skill, though, if you don’t use it, you will lose it. Now our focus is to get him to catch up in reading and writing English, since he CAN hear well enough to use it, and at this point, teaching him ASL would alienate him more than he already is. We have tried to use fingerspelling as a way of reinforcing his spelling skills, but he has problems with fine motor control, too, and finger-spelling is very challenging for him.