dtach does not influence OS resources in the sense that it reduces RAM or CPU cycles, dtach detaches a process from it's parent process. renice on the other hand increases / decreases the priority of the process for the schedular; the process will gain more cpu-cycles .
So: yes, you can use dtach to detach evince from your xterm (I doubt that you open evince via xterm anyway). This would only ensure that closing xterm won't close evince. Yes, you can renice a lower priority to evince and then the scheduler will call evince less often. Memory wise there won't be any change at all. To reduce work load you might minimize evince so it is not visible and thus nothing new will be rendered and no checks against overlapping due to other programms will take place.
But, and I mean that in all seriousness: Stop fiddling around with your system in such micromanagement style and just buy more RAM. As long as you don't open 1000s of evince to be read later (which is a usage pattern I would change in the first place) the OS will behave not really differently when you microtune the OS. If you don't want to read the .pdfs now: save them to disk. Problem solved.