No. Once a block is on, iPhone keeps it on, even if you swipe Slow Time Club away or restart your phone. You don't need to keep the app open.
Good to know
Quick Blocks, Focus Sessions and App Limits all keep working while Slow Time Club is closed.
One backup timer inside Slow Time Club, the one that ends a break exactly on time, pauses while the app is closed. Your "Break's over" notification and iPhone's own timing still work.
If anything looks out of date, open Slow Time Club and it catches up straight away.
If a block didn't start, end or come back when it should have, go through Blocking isn't working: start here.
Still stuck? Contact us from Profile → Help and Legal → Contact support and include your User ID (Help and Legal → User ID).