Hi Sam,
You need a GMF voucher to be able to eat GMF breakfast at the restaurant in the park which is open for GMF. This is usually in Fantasyland. You can only get a GMF voucher in exchange for a normal breakfast slot taken at one of the designated onsite Disney hotels. So, if you are not staying at one of the designated onsite Disney hotels, then no, you can't eat breakfast in Fantasyland during EMH, even if you have a Dream AP.
You can, as Small World has said, eat at any of the restaurants in Main St which may be open during EMH.
Elaine