yes. there are plenty of very good "teach yourself" packages about. I myself am currently learning 3. The process involves having a thought along the lines of "You know, I've always fancied being able to chat up those Polish honeys in their own language", and then acting upon said thought.
Mate, it all depends on the defence requirement. There are a few languages being taught right now that fill MOD requirements and I would imagine you can express a preference but there's no guarantee whatsoever you'll get the one you want, unless you're desperate to learn Pashto of course.