I can only speak to the American system so i would appreciate folks from other countries weighing in.

In a roundabout way - yes. Under American law, you have the right to vote as long as you are 18, registered to vote, and not otherwise disqualified. Any disqualification cannot be based on a poll tax, race, or gender. You can however be disqualified if you are convicted of a felony. Different states handle this differently with the disqualification being permanent until pardoned, or the disqualification ending a certain time after the sentence is served or immediately when the sentence is served.

The connection to the draft is straight forward - the United States currently does not employ a draft BUT does require men to register for the selective service - which would be used to re-institute the draft if one was needed. Failure to register disqualifies the person from federal student aid and governmental employment. Further, while I am unaware of how frequently this is enforced, failure to register is a felony. If a man refused to register for the selective service on the feeling that he would not want to be drafted should it be re-instituted, he could be convicted of a felony that would affect the right to vote.

It also bears mentioning that when there was a draft, dodging it has always been a criminal offense which is why the draft dodgers who escaped to Canada had to be pardoned before they could return.