No, it's because all the Orthodox that existed in cities realised the schism was stupid. Most of the 'Old Believers' moved to whatever remote part of Siberia or Alaska long before the communists existed. And those that do still exist, live in a timewarp, and are more akin to a cult than an Orthodox community. Keep in mind the schism happened in 1666 - nearly 3 centuries before the communist revolution.
https://en.wikipedia.org/wiki/USSR_anti-religious_campaign_(...
Here is another example of a community of old believers in Alaska (1968) with an article in the Atlantic: http://www.theatlantic.com/national/archive/2013/05/a-17th-c...
The main reason for persecution was the old believers distrust of state power. They didn't accept rule by it and they didn't take any part in it. They were similar to the Amish people in the US.