Can I use an old iMac as a display for a Mac mini M1?

no, well not as primary display anyway

there are third party options Use iMac as monitor: 5 Solutions - 9to5Mac

though a real monitor would use but a fraction of electricity compared to a full imac computer displaying for another computer, and the performance would likely not be good enough for games or video

Not as a Target Display. Even if the old iMac is so old that it supports Target Display Mode, Apple added restrictions on the video source that mean that no current or recent Mac (such as a M1 Mac mini) supports using ANY iMac as a Target Display.

For the PRIMARY monitor on a Mini you must use a proper external monitor. The workarounds are too laggy to use as a primary monitor and may not even display video content like video-conferencing properly.

One of the workarounds, Luna Display, has this on their support home page:

The red emphasis is Luna's, not mine. That says up front that an iMac on Luna is good as a parking space for static items like open windows and app palettes but not as a main monitor. Other "fixes" suffer similar handicaps.

Save yourself a lot of grief and expense. Get a free-standing external monitor. You need one to set up the Mini anyway.