Okay so I've just started a new character.
I've decided not to do the main quest for a very long time, and I'm leaving it so that I get no dragon attacks. I had them so often on my other game I'm just sick of it.

Okay, so I'm going to be a pure mage.
Will I be able to keep up? Will everything be as weak as me?

Tips would be appreciated.

If you don't power level with smithing and enchanting or (alchemy like others claiming its an exploiting) then it would be fun to play as pure mage for a while, when you got all mage perks the game will become too easy in all difficulty modes hehehe.

Edit: Mage is quite too over power and best surviability to all encounters in skyrim.

The main factor will be what difficulty setting you play on. If you play on 'Novice' you will kill everything easy with 1 or 2 fireballs.

^^This but even at master mode...I can kill a dragon less than 30 seconds O.O