Is this ever advisable? Would it be, say if I just wanted to send and receive small messages using the standard SMS on the phone and sending and capturing those as as a way to communicate between two devices on my app? The app is open on both devices while messages are sent. Or what would be the potential problems with this and what are better alternatives?

Yes it should be possible. It is advisable? No.

Why not:
1. SMS 'protocol' does not guarantee that the message will ever be delivered.
2. Text messages often take up a lot of time to get delivered. So this could lead to out-of-sync problems. Say you sms question 1. The receiver sends answer 1, but it gets stuck in the network somewhere. Now you send question 2. Now answer 1 is delivered to your telephone and appears as an answer to q2. Do you understand what I'm getting at?

Better alternative IMO would be: e-mail. Email will always be delivered when both emailserver are up. (the sending and the receiving). Blackberry already has an app with this. I think it's called blackbarry chat/blackbarry talk or something