Anecdotally my experience would suggest that they are important. As someone living in one European country where English is less frequently spoken and occasion

Anecdotally my experience would suggest that they are important. As someone living in one European country where English is less frequently spoken and occasionally traveling for work to others where English is more prevalent, I always felt that I could notice a real improvement in my second language upon returning "home" after speaking English for three or four days. Incidentally, those same breaks usually resulted in improvements in rock- climbing (which are a bit easier to measure objectively because of the grading system), but I tended to attribute that to a full recovery / perhaps I was over-training. Thinking about it now, maybe it's odd that I always accepted that the stenuous physical activities naturally needed a recovery period while assuming that I could just keep hammering at the mentally taxing skills day after day.