I know that Anki is absolutely hell when you don't do it everyday. I'm wondering if it's the same for Renshuu (I hope not!) because I'm actually going to miss a day lol.
I've never had Kao-chan come to my house and beat me up for missing a day, or anything like that. The only thing that has ever happened is my backlog of terms that are ready to study builds up. If it bothers you, it will eventually go away as you put in effort and the terms rise in mastery.
If you every feel overwhelmed, in the schedule options you can reduce the number of new terms you get, and if you need time off you can freeze the schedule there too.
If you know you're going to miss studying for a while and don't want reviews to build up, freezing your schedule is the way to go (it basically pauses it so you don't accumulate more reviews).
You can also go into your schedule settings and give yourself a daily goal instead of using the "study as much as I can" option. This makes Renshuu give you the same amount to study every day, so even if you're drowning in terms that are ready to review, you're only prompted to study as much as your comfortable with.