An L5 with a built in humbucker wasn't really designed to be an acoustic instrument. A guitar amp wasn't designed to produce much outside of the midrange frequencies you get from an electric guitar. So, while you'll get a nice sound, one which people expect and very much like, it won't be pure acoustic.
Of course if you go down the path of a real acoustic sound (carved archtop with an unimpeded top, acoustic strings, acoustic pickups and/or mic's) you'll likely feed back so bad that your bandmates will not be happy. That and I doubt anybody will appreciate the nuance outside of a solo guitar setting.
If it's bothersome, you could try a Charlie Christian style pickup (they come in a humbucker drop-in format). IMHO, quite a bit more acoustic sounding than a humbucker. You could also try a K&K Definity pickup mixed in or a DPA mic.. but I think you'll find it's an awful lot of hassle compared to the one guitar, one amp approach.
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Spook
Southern Oregon
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