Keyboards have been able to sound like other instruments for a long time now, even drums, and in fact, routinely do sound like strings or horn sections. With electronic drum sets, it's easy to make the same drum pads sound like different percussion sounds, but you can also make them sound like other instruments if you like. The about-to-be-released You Rock guitar finally makes guitars work the same way: its strings are actually string-like buttons, and though you play it just like a guitar, its sounds are electronic and can emulate the sound of any of dozens of different kinds of guitars.
Of course there's no reason it can't sound like a horn section, or even a drum set. So imagine a band where the drummer is playing electronic drums that sound like a bass guitar, the bass guitar player's guitar sounds like synthesizer keyboards, the keyboard player's keyboard sounds like a guitar, and the guitarist sounds like a drum set. Now that would be a weird little gimmick!
Of course, some instruments are better suited to some sounds than others. The drummer playing guitar couldn't bend the string and is limited on how many notes he can put into a chord, or how many notes he has available. The guitarist playing drums would find it hard to manage the distinct rhythmic signatures of the different hands and feet of a drummer. One would have to compose or select songs carefully to make the combinations work.
If you're looking for a really weird gimmick to get your band some press notice, though, it might be a niche market that could attract some "Oddly Enough" news. Unless maybe someone's already done it.