Yeah, they do, now. "Asa-Makku" ("Morning McD's") came to Japan in 1994, as near as I can remember. When I arrived in 1993, there was no morning stuff. Japanese people would visit McD's at 7 a.m. and get a hamburger and fries. It was oddly disturbing. When I moved to Kyoto in 1994, the McMuffin had appeared, but some McDonald's were not carrying them.
Unfortunately, instead of the McBiscuit series, those loathesome McGriddles were instead brought over.