It really depends. If you already have some 85s and are rolling an alt, yeah, you probably can get 20 fairly fast. You'll be power leveling through things, knowing where to go exactly, etc. I you are new, take your time, actually read the quest text, get into the story some, explore, work on professions like fishing cooking or mining, etc, it will take longer.
I'm working on a new character on Alliance side, and am at level 12. Even with the + 10% xp perk from my guild and the + 10% bonus from spinning around the maypole for the midsummer festival, it's still taken me about 7 hours /played.
And Chief, are you sure you have to start paying at 20? The way I read it, you just stop leveling just as if you were on the trial and hit 20 before the time limit. So at 20 you could still explore around and do other things even if you couldn't level if you didn't want to buy the game.
But yeah, if you do recruit a friend, you will hit 20 very fast with the triple xp.