I haven’t done this myself, but I assume you can turn off the display in Desktop Mode. I assume somewhere in the “normal” Linux settings there will be the usual Turn Screen Off after … and Go To Sleep after … You could just set the screen to turn off after 5 mins, then set sleep to never and that should do it.
I’d assume it won’t, you can always just test it out though. There might be some setting for those timeouts in the Steam-steamdeck settings.