Actually, if you play War of the Queens as written, a Gaim PC would be VERY difficult. If I remember correctly, any Gaim at all brought within range of the mad queen would go mad itself and probably turn homicidal, or at least be very very crazy.
On the other hand, it'd be the perfect place to pick up a Gaim PC AFTER the rogue queen was dead. Though I doubt the rest of the Gaim would take that very well.
On this topic...how would an erratic Gaim work as a PC? Wouldn't all the Gaim be gunning for it? In a rogue party running a more Freedom Station/Firefly/Bounty hunter style, I can see it, but any group that docked w/ B5 would probably have hunters and political pressure to deal with. (Unless I'm wrong on how the Gaim handle rogues)
If I did allow a Gaim PC, I think I'd be fine with a non-erratic. The Gaim hive mind appears to be complicated enough to simulate free will (look at the Gaim ambassador's behavior on B5), so a PC who wanted to play one could probably do whatever they wanted, so long as they kept some general guidelines in mind (like the compulsion to try to make every situation pay off for the Gaim, or to never knowingly harm Gaim interests)