I ask after encountering the following sentence in Tatoeba:
Yes, your guess is right. However, I think you should focus on the character "再" here. There are several such patterns with "再".
The pattern "再 + verb + ,  + 就 + " is used to express a condition, a premise; remember that "过" here means "[time, etc] to pass, to elapse" and "再" means "to continue to do something" or "to do something again" here. This pattern is somewhat like the pattern "if sb/sth continues to do sth,sb/sth will..." in English.
"再" here implies "you" have covered a distance already, so now you continue to walk.
"再" here implies "I" have written for a while, so I want to continue to write.
"再" here implies "you" have harassed me for some time, so now you continue to harass me or harass me again.
When a police officer is chasing a criminal, he would warn the criminal,
Even without 再, it still means "in [amount of time]". For example, "过几天" means "after a few days".
I don't have any statistics, but yes, I think that using 过 is the most natural and common way to express this concept.