Yes, I have the lowest rate (LTV <50%) of mortage interest, and I have freee banking with them.
When you open or transfer your mortgage to their LTV mortgage you have to open a current account to service it. You have the choice of their 4 (iirc) current account types. I chose the free banking one (I think it's called Easy).
The only drawback of this account initially is that they do not pay your house valuation, whereas if you choose one of the fee paying accounts you get €100 towards the valuation. I think one of the fee paying accounts also pays interest, but in any event, all the info I was given was exactly the same as their leaflets, and their website.
Regards