I have a 77 templar on PvE, and he's speced for 100% melee crits so I do consider him a batle cleric. When I rolled a healer on PvP though, I picked a fury. I don't think I've ever seen a cleric successfully solo in PvP on a consistent basis. So it depends on whether you intend to solo or group.
In a group, your plan is very viable indeed and you'll be welcome simply because PvP is overcrowed with druid healers. But like the emote says "you gotta sleep sometime". Well, in this case, you gotta travel sometime, and you can't always take a group with you.
You main conumdrum is going to be "how do I defeat swashies and rangers 1 vs 1?". That's gonna be tough with an inquisitor. They might seem like only 2 classes, but sometimes it seems that's all Qs roll

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I don't know enough about the Inquisitor AA tree to help much but maybe someone else can.
You say "battle cleric" to you doesn't mean melee. But I think you should reconsider. When my templar is buffed with over 500 STR he can do some nasty damage on autoattack. Nothing to be sneezed at when you can heal yourself with reactives while doing melee damage with no power cost.