Is it possible to have user prompts while running from an unattended bot runner?

You can use user prompts while running the bot in unattending mode. But when using intervention is needed to provide input then it is meant as attended bot. Although Attended bot in A360 has whole new features AARI concept.

So then if a prompt pops up on an unattended bot runner machine, someone can't go click on an option to resume it?

User should have access to the bot runner to provide user inputs for the bot.