Can I PvP as a protection paladin?
Yes, but not very well.
Since the nerf to our incessant selfhealing we became a lot less viable in arena. Battlegrounds, however, are a slightly different matter. Especially if we gear up as well as possible.
Now, being well geared isn't the same as showing up in your mid 350 tanking gear and thinking that it'll work. Casters will hand you your rear and even melee will be sadly uncooperative. By cooperative I'm referring to standing in the front of your shield like the targets you usually tank.
You'll need proper PvP gear, and that's easily gained from honor points alone. As we're likely to focus on getting our tanking gear come 4.2 the state of the art PvP equipment won't come fast. However, if you just happen to sit on a few thousand valor points you could as well convert them into their conquest counterpart and get started.
You want exactly the same gear as a retribution paladin, barring a one hander and a shield. Both are, luckily enough, available in PvP versions. Start with a trinket that gets you out of trouble once every two minutes, and try to get the gloves as soon as possible.
Now, somewhere above 3000 resilience the fun in battlegrounds start as a paladin tank. You'll primarily concentrate on carrying flags, defending objectives and tank the ocasional boss fight that occur. The latter is better done in your proper tanking gear though.
You'll soon notice that players are surpricingly easy to taunt. For some reason a lot of people take personal offence at someone who refuses to die instantly. If you back up into a corner you'll even be able to benefit from some of that shield blocking that is part of our normal procedure. However, you can't fight ranged opponents from a cornered position. Those need to be handled by either a corner pull or an outright assault.
Another fun job is the deliberate suicide, especially if you happen to have a healer who likes you. Just head into the thick of things and start using AoE like you were tanking trash. More often than not you'll get the attention of enemy players who start hitting you instead of doing something useful. A few heals are usually enough to keep people occupied for well over half a minute, which is time the opposing team sorely lacks.
Never expect to get a decent kill score. That's not your job when tanking, and that's not your job in PvP. You're there to be a meatshield and a general PITA.
There's even a marginal profit for your tanking to be had if you're inclined to push out as much damage as possible on content you overgear. The PvP gloves add a sweet 5% damage to all your CS attacks.
Also, if you're grinding materials, most likely as a miner, and play on a PvP server, gear with resilience will make ganking you at a node all that much harder. In a one one one match against someone who's hunting players in the open world you're very likely to come out victorious. The main reason isn't that the protection paladin is so fantastic at duels, but rather that gankers tend not to be overly well geared, and as a tank you're already a lot harder to kill to begin with. While you do pitiful damage you can usually just outlast your attacker.
The last, but maybe most important benefit, is that you'll grow a new kind of awareness to your abilities. When to use them, and how to use some that doesn't see as much use when you tank as they ought, well, at least not as a pugging tank. Removing snares, shielding that friendly healer of yours, swapping seals midfight, using trinkets, using potions wisely and pathing.
Pathing is knowing which way you're going to move, before you move. As a protection paladin you're suspectible to all kind of bad things slowing you down, but you move faster than most other players. That makes moving intelligently all that much more important.
Oh, and fighting with the information from your screen. No DBM telling you when to use what abilities. You'll need to act upon a lot more of the graphics that is provided by the game rather than addons.
Now go out and have some fun slamming that shield of yours into the face of other players!