From what I understand, there is connection inasmuch there is genetic commonalities between all Native American peoples and the East Asiatics--the Native Americans were descended from a series of migrations that flooded into the Americas during the late Pleistocene/early Holocene.
Cultural similarities are definitely present, but one must be careful of drawing too many conclusions from scanty anthropological evidence. Indeed, modern Ainu culture is undoubtedly not identical with previous Emishi societies. Changes have been inevitably wrought upon the culture as a result of time, war, and other factors. Culture is never perfectly continuous through time, although they have undoubtedly preserved a great deal of their ancestor's ways of life.
It is not accurate to compare the Ainu to Native Americans, as some might be tempted to do. Rather, the conquest of the Emishi during the 8th century was more akin to the Roman conquest of Gaul--military rule coincided with the cultural assimilation of the conquered, and the investment of the conquered into the new regime. Hence, the Emishi became integrated into the Fujiwara regency of Tohoku. Those who didn't want to assimilate moved to Hokkaido and became Ezo/Ainu, where they later suffered further losses to Japanese colonization during subsequent periods.
Hence, to identify them as the indigenous people of Japan isn't entirely accurate--they are descended from them, inasmuch as they are descended from the Jomon and subsequent Emishi peoples.
Bookmarks