Sure, if Democrats could prevent middle class whites as a group from voting, they would; they can't. Replublicans absolutely can price poorer black people out of voting.
They don't have to do anything as complex as voting at several polling places. They just have to go vote once. That's easy to justify to yourself.
It's a massive opportunity to cheat.
They definitely do not vote! There are more published examples of Republican politicians illegally voting than there are of illegal immigrants voting.
There are lots of places where illegal immigrants can receive drivers' licenses and other forms of government assistance. And they do. For example, just in California, there are now a million illegal immigrants with driver's licenses. [1]
"Through June 2017, the Department of Motor Vehicles has issued approximately 905,000 driver’s licenses under Assembly Bill 60, the law requiring applicants to prove only their identity and California residency, rather than their legal presence in the state."
In California, a driver's license is enough to vote. In fact, it automatically registers someone to vote.
[1] http://www.sacbee.com/news/politics-government/capitol-alert...
Or are you calling "connections to citizens who can vote legally" a massive opportunity to cheat?