Yes, the ODJB was influential, first because they recorded early and second because their recordings were fairly well distributed.
But there were plenty of hot bands up and coming in the South and in the Midwest who surely did not spring full blown in the early twenties merely from hearing a handful of the ODJB's records.
You also have to consider the person-to-person, ear-to-ear transmission of the hot style which quickly spread in every direction because it was so good, so infectious, that people naturally wanted to hear more. Part of the spread was because of easy transportation, along the big rivers and by railroad, for jazz players; part was a result, as Muldaur touched upon, of having a waiting base of youngsters with access to instruments and lessons, a grounding in American music, and a few quarters in their pockets to pay to hear more, so that playing hot music came naturally to them. Being Americans, they also had the urge to follow wherever the music led and it usually led to the cities.
The ODJB was an impetus, but was already part of that process as well.