Initially, yes. However, your PvP character would be level 20 with full attribute points. You can then use Bathazar Faction to unlock any further skills and/or items you want for your PvP character. Once a skill or item is unlocked, you can add it to a skill bar or equip it onto a PvP character.
Your next question would be: "How do I earn faction if I don't have the skills and/or items to build an effective PvP character?" The answer to that is not as easy. The best way is patience and practice. If you can get to the Zaishen Challenge and Zaishen Elite, you can practice there and earn up to 2,000-6,000 faction per day fairly easily until you can unlock enough for a more effective build. Trappers are an effective build to do this. There are usually groups looking for more trappers to do this. Ask in alliance chat too, someone might be available and willing to go.
The last steps are the hardest and there is little others can do to help with the first one. If you don't have Heroes' Ascent unlocked already, you will need to do that by first winning 5 consecutive matches in the Random Arenas (talk to the Canthan Ferry Captain on the Isle of the Nameless to get there). After you have one 5 consecutive random arena wins, you will need 5 total (not necessarily consecutive) wins in the Team arenas. This will unlock Heroes' Ascent. This process should earn you enough faction to get a few more skills and/or items.