I tried this once with MBNA. To get their free offer of "his & her watches" (don't take this piss, yes they have not moved from the cupboard i initially put them in) i had to make at least one purchase > 10.
I used the card once to fill my car up at about 25 and once the transaction registered i paid off the amount outstanding and transferred my balance. I still get charged 34pence each month for my first transaction. I think they claim that any payment made during the month is put towards the payment on the end of month statement, and because my transfer also took place within that statement my first payment was used against the 0% offer. So i needed to wait until my statement was produced before doing the transfer.
I read the Egg offer terms and conditions to mean this was well. I could be wrong and the wording is not conclusive.