This partially depends on whether you mean for a PvP or PvE character.
For a PvP character, yes, the purchasing all skill packs will allow you complete use of all campaign skills in PvP.
For a PvE character, no, as PvE-only skills, cannot be unlocked via skill pack purchases. So, for example, you'd still have to do quests for the various factions in Eye of the North to get those skills.
Note that for PvE characters, this doesn't mean that you automatically will have all these skills learned on your character. You will still have to pay to learn non-elites and capture elites. However, non-elites will be available on all skill trainers for you, which can be especially valuable in the early game, where the skill trainer's offerings are more limited. You can also learn unlocked skills through elite/non-elite skill tomes, and, perhaps the handiest feature, all unlocked skills will be available for you to equip on your Heroes.