Do the M1 Macs "shutoff" RAM or CPU Cores?
No, the issue you're seeing is not in any way caused by the M1 "turning off memory" or "turning off cores". It is entirely caused by the manner in which this particular software program is structured.
Remember to check your BOINC settings - you can actually decide how large a part of your RAM that BOINC can use. The lower you set it (all else being equal), the more you'll see "Waiting for memory".