No matter how voting is done, higher income people will vote more than lower income people will. The reason for this is that higher income people feel that they gain more from voting than lower income people do. They feel the satisfaction of participating in a system that works for people like them. Lower income people are less likely to feel this satisfaction.
Now, if you are asking whose turnout will be increased more if absentee ballots are used, it will likely be lower income people. They gain lower benefits from voting and so they are only likely to vote if it is made easier for them. High income people feel good about the system and are likely to vote no matter what. Low income people get lower benefits from voting so they are more likely to vote only if the costs of voting are lowered.