Sure, but do they multiplay well on many of these smaller <4" handhelds?
Can't say for emulators, but I have playtested a couple of multiplayer games with my brother using Dingoo <-> Dingoo connection (yes, Dingoo supports multiplayer via usb networking with a PC host in the middle). We have completed the whole Doom I&II on coop mode, which was a really awesome experience. Besides that we have also tested Jazz Jackrabbit and Descent 1&2, which were ok, but not as epic as Doom.
As for Quake, currently there's a bug in the sdlquake preventing a player from joining a hosted game, but I have seen a patch for it somewhere.
Duke3D desynchronizes too fast, but eduke32 devs are working on a new multiplayer code which should play just fine on handhelds.
I have said that many times already, but I really think having an easy way of multiplayer connection (wireless or cable) between two handhelds can be a good selling point. Especially if the console itself is cheap enough to buy them in bundles