the prices you pay for mobiles on ebay aren't worth it half the time.
In theory it should be ok, yes pop your sim in and carry on with your old number.
But.... It could be stolen, it will DEFINATELY NOT have a warranty and...
If it gets reported stolen or claimed lost on an insurance claim it will be barred permanently in the UK from every single Network.
A guide second hand price for a d600 would be for me around £90 to £100 inc. delivery maximum. They can be had now on PAYG for £160ish brand new.