Time does not gate acquiring BiS gear at max level. The weekly lockouts is what does that.

With that in mind, based on the free time you have to play the game, it is more than adequate to take full advantage of your weeklies. How many weeklies it will take to gear up will depend on how many roles you want to do that with. I say "roles" because jobs within a role can share the gear except for weapons, so yeah you basically nailed with it being 1 tank, 3 DPS, and 1 healer as there are currently five roles. However, within the Melee DPS role, there is Striking, Scouting, and Maiming sets, and within the Ranged DPS there are the Aiming and Casting sets. That would bring the true number of sets you can acquire to seven.

Due to weekly lockouts, I don't think there is enough weeks between patches to BiS everything, but someone can correct me if I am wrong about that.