I have two alts that I play in dungeons, a DK health tank, and a Templar healer. They are both leveled in the high 30's, and the builds I am following say that both of them should have Aggressive Horn as ultimate on their second bar. I have been putting off going to Alliance War and leveling Assault Skills. Today I took both alts to Alliance War, kept saying "lfg" in group chat - and got invited to join groups. And it didn't feel like a grind before I leveled Assault Skills to level 4 for War Horn. Probably two hours on each alt.
Many thanks to the two groups that allowed my PVE build alts to tag along while they traveled around the map capturing resources and keeps. I still have open character slots, perhaps someday I will build an alt just for PVP.