Yes, you can, and yes, they will cross breed.
I'd make sure you have enough standard sized hens for a standard rooster, so he doesn't spend all his time squashing banty hens.
I have 8 large fowl hens, 1 large fowl rooster, and am adding four bantam pullets and a roo (along with five more large fowl) pullets. Right now the youngsters are segregated in a small coop with an attached, covered pen, the whole thing is inside the big chicken run. That way they see and hear each other all the time. Yesterday I opened the interior, adolescent chicken pen and the large pullets and rooster visited the kids. Only one pecked at them, but she's the usual suspect and low on the pecking order (so she had to let the kids know SHE was more important than THEY are). Then the Big Chickens lost interest and went on their way.
This weekend I'm going to let them all mingle; the kids have been out there about six weeks now (and are about 14 wks old).