Yes! Although, (a common theme), it was nowhere near as exciting as in Malory Towers etc. Certainly no shimmying down drain pipes .
What would normally happen, is someone would be homesick/fall out with friends/have argument with housemistress and they'd declare they were running away and then they'd hide somewhere in the boarding house .
People (at least in my time) rarely absconded during the night because it was in the middle of nowhere, and a creepy walk to get to a road, and then if you could get a bus, it would take you to a sleepy town that was equally poorly served by public transport. If they did 'escape', then they'd usually be back in 10 mins, before anyone had realised.
People fantasised about running away a lot, but I think maybe 2 people ran away 'properly' whilst I was there - both older, one wandered off on our weekly health giving walks and got rounded up by teachers a few hours later following tip off from local farmer, and another managed to get home to London, I imagine with external assistance.
A few times, we'd have a panicked house mistress asking people when they last saw x but generally, they were either found in another boarding house or had missed bus (pre-phones).