I don't know the answer to this, but personally I would refrain from allowing the DVR to sleep. If you use tuner sharing or any internet streams (TV Everywhere or Custom Channels) you will have a poor experience, as your client won't be able to watch on demand because the DVR is sleeping and not responding to requests for data.
I'm not sure if it's drastically different on the Mac, but in general the DVR should run at startup. The DVR itself is quite frugal on resources, so working while it runs in the background will be fine. (You may notice a slowing if you have remote streams transcoding will you're using the computer, but it's relatively negligible.)
Also, let me chime in as another to recommend the Apple TV route. The UX is far superior to anything that Android can deliver. This is not just for Channels, but I find that the tvOS version of other software (Netflix, Hulu, etc.) to be far superior to the Android counterparts. Of course, this is all IMHO, YMMV