Is it possible for an Archer to get by without using any Melee combat. I'd of thought it would be possible as you can bash enemies that get too close with your Bow then step back and fire off a shot. Obviously taking a perk like Power Bash would enhance this further?

If you invest heavily into archery perks, have a good bow and arrows and are a good shot I don't see why not.

Melee shouldn't be needed, though i still keep my 1h weapon at a decent level just in case i run out of arrows when running around.

I regret investing two points into One-Handed, zero-point shooting hits harder than melee.

Assuming you're not exploiting Smithing/Enchanting then I would have to say yes UNTIL you get Ranger, Power Shot and Quick Shot. The simple fact is that you can go into melee whenever you need to, and you WILL need to before you get the aforementioned Archery Perks (and Deadly Aim), it just won't be as effective as your bow unless you invest Perks in it. If nothing else, though, the ability to put your bow away and lop off someone's head is pure awesome. Once you can move and shoot fast and you're staggering your opponents half the time you shouldn't need to go into melee with anything but the toughest (and fastest) opponents unless you want to.

As an archer, melee shouldn't really be needed. The only time I ever find myself drawing a blade is if I've somehow found myself surrounded by multiple (usually 3-4 or more) enemies at close range, that I have no choice but to hack and slash my way out of. That's pretty rare though.

If I'm at close range with one or two mobs, my bow is still enough. Perks like Power Shot (stagger opponents) help a ton. I haven't gotten up to Quick Shot or Bullseye, yet, but I'm betting that would make it even easier.