No, it is not "just like trading without Level II". Whether you use Level II or not, you know what the published bid and ask are. The MMs who publish them are required to honor those prices for the sizes indicated. In addition, they can move the bid and ask to make either or both more attractive to players. Also, they can sell (or buy) naked to meet demand.
With Greys, the MMs are facilitators at best. If a broker is unable to cross a trade, if he feels like it and has time, he'll call an MM or two, asking if they can match his client's order. But the MM is not obliged to do that. If he wants to take the trouble, he can try to come up with a match; if not, he doesn't have to do anything at all.