Is it possible to get BasicTalk working on my OBi200? That way, I won't need two ATA's connected to my router.
No, at least, not without some serious TOS-violating hacking. Vonage (BasicTalk) is a SIP-based VoIP provider, that offers unlimited calling. To protect against abuse, (e.g. people sharing their unlimited calling with another user), they do not provide users with their SIP login credentials. The service requires that you use their ATA, which is "locked" to their credentials.
If you want to keep your service with BasicTalk, then great; just live with two ATAs, which consume very little electricity. Otherwise, you may want to consider porting out your BasicTalk number to another SIP telephone service provider that offers "Bring Your Own Device" service (that is, they will provide your SIP login credentials). In that scenario, you could provision the other SIP service on the same OBi as you're using now.