Does HostHorde support non-vanilla servers?

Yes, you are free you use custom server JARs, including, but not limited to:

• CraftBukkit (including unstable beta and development versions)
• Spigot
• Forge, including Tekkit, Feed The Beast, Pixelmon, etc
  
• BungeeCord (as both a hub, or servers in a BungeeCord network)