That is a great call, an atom would struggle big time running plex, I have a Thinkcentre M92p which is tiny and silent, do wish it had a tiny bit more grunt but was pretty good value for $200.
I had an older Atom device running Plex server for quite a while, but back then I almost never needed full transcoding for playback -- usually 'stream direct' which just shifts the MKV container to MP4 -- relatively easy work. And when I did have full transcode, it was either from h.264->h.264 with slightly different profile settings or MPEG-2 -> h.264. I had to configure it for the lowest quality transcoding settings in order to avoid interrupted playback, but it worked. I upgraded to fastest i5 that was offered about two years ago and it's handled everything quite well -- though h.265 transcoding takes substantially longer to start-up and seek than h.264 full transcodes.
I'm curious what modern Atom processors can handle. I know they've made some improvements to the chips, but is it enough, yet?