There's definitely a place for upright basses but sometimes you have to compromise - especially if you don't have the specific expertise required to make them work in a live context. That's by no means a criticism - I've met plenty of sound engineers that struggle with them and I wouldn't want to use one unless it was necessary. Most of the time I've found that using a normal electric bass with flatwounds and/or with the tone control rolled back gets you most of the way there.
A few years ago I had to play as part of an acoustic Jazz quartet for a recital. The lead was flute, with piano, bass and drums. The bass player ended up just sticking with his Tokai SG copy - partly because it was easier to play and partly because it was a lot of work making
any kind of upright work. Electric uprights are great but they do require a lot of practice. The other option is a fretless bass, which sound great but also require practice to play and are usually associated with a particular sound - back in the 80s players tended to use a lot of chorus and I still think there's a bit of a hangup there for some people. For the record, I love fretless bass and there are definitely things that you can do with a fretless that you can't do with a fretted bass:
http://www.youtube.com/watch?v=nAgd9Ijw6WI
You can really go mad with the vibrato and slides!
There's definitely a visual reason to want an upright. They look great in the right context and if you can play them well and make them work then there's no reason (other than expense) to use one but the two prerequisites alone make them quite rare. Thinking back, I can only remember one gig (a psychobilly band) that made the upright work well and even then there were problems with the pickup.
Also, if your bass player does consider an Asbory, I have three bits of advice. First, talc your hands before you play - may sound odd but the strings stick. The manufacturers actually recommend this. Secondly, make sure that you have several 'G' strings available. Buying them in two metre or six foot lengths is advised (you just cut it and knot it at the bridge). The Ashbory has a tendency to snap the 'G' and I've experienced this - it's a pain. Thirdly, let him know that the fret markings aren't very accurate. They give you a rough idea but unlike a normal fretless (where you can just use your eyes and fine-tune with ears) you have to really listen to make sure you're in tune. They're quirky instruments and he'll need practice to be able to play it. It's not just a case of buying it and coming straight to rehearsal - especially if you play anything around the 12th fret or higher. Finding the 12th fret natural harmonic might give him a better chance of knowing where the octave is - might even be worth marking it with a bit of tape on the fingerboard.