The CoE doesnt need to be baptised.
Of course, it depends on the individual priest, but the general rule is that to avoid any trouble, you should be baptised and should agree for the children to be raised as Catholics. You might find a liberal priest who is willing to ignore this - but it's by no means certain, and it may require special approval - which given the processes of the Catholic Church, it's by no means certain that it will be granted.
I know that many priests simply wouldn't agree to marry an athiest in the church.