Guns of Icarus Online and Guns of Icarus Alliance are connected with each other and technically they launch the same application and you can switch between two modes without leaving the game. Some of the players do have the expansion bought, but still prefer PvP like I do.
So do I. I play Alliance every now and then, but like playing GOIO as well (to play with some friends who dont own Alliance). Actually, I find a lot of players in GOIO skirmishes who own Alliance.
The cool thing is that while playing skirmishes I still gain reputation for Alliance
So don't worry. If you don't want to buy Alliance for now, you'll still be able to play with everyone else. Still, consider buying Alliance in the future: it adds a lot of extra fun