...no.
Although you could run Palkia lock without Garchomp. You will just have to really focus on a single Palkia G Lv.X and basically block out everything your opponent is throwing at you with something like Sableye/Smeargle start, Initiative, Judge, Giratina Let Loose, Chatot G, Mesprit, Power spray, Spiritomb spin (oh the extremes). It's a deck that can basically get 3 attackers out (2-2 Palkia, 1 Aaron). You'd run Garchomp but you just can't get it fitting in there.
Luxray will just make you cry if they manage to get past the disruption barrier you'll be throwing at them. Otherwise, this variant can rock.