I don't think they'd massively ramp up incarceration in response to not being able to disenfranchise people. The reason isn't because they're nice, it's because people generally take "the path of least resistance".
For example, if there's an easy way for someone to do something bad, and you prevent the easy way, people might counter-claim that "yes but there's a hard way to do it too, and everyone will switch to doing that if you block the easy way!".
But people don't actually think like that. They'll switch to doing something else entirely that's also easy, unless they have absolutely no other choices. (For example, if people are doing easy PKs in an online game, and you make that a lot harder to do, then most of them will in fact just switch to playing an entirely different game rather than game the now complex effort of being a PKer in your game. This is something game developers somehow get surprised about: they remove the exploity behavior and expect the wayward players to either become "good" players or get extra-sneaky in response. In fact, most of the exploiters just stop playing the game entirely and do something else with their time, hence the big player numbers hit if you enact this stuff that's supposed to make the game better for everyone).
So, say that arresting someone on a low-level felony and putting them in for 1 year means you've prevented them voting for conceivably the next 40 years. If you can't do that, I doubt it would be cost-effective to arrest and lock up 40 times as many people to get the same effect. In fact, that would blow out the court system and those arrests would take years to process, meaning the felony convictions would take far too long to strategically impact the next election.
In fact, they may respond by lowering the emphasis on pushing arrests, since those require cost effort, and they're now delivering only 1/40th of the effect on votes as they did before. Think about every pro-Republican prosecutor now working 40 times as hard to push convictions to get the same effect as today. They would quickly see it wasn't worth it, and they party would totally change tack on this issue. If something becomes 40 times less effective at achieving the stated goal, people don't generally do it 40 times as much to compensate, they do it less than they were.