Plex server does transcoding to send compressed over the internet. However I think there is an option to do minimal transcoding but that used more bandwidth. but I don't think a this joke of a CPU will be able to handle it.
https://support.plex.tv/hc/en-us/articles/200375666-Plex-Media-Server-Requirements
1743 Passmark score. I think in general people are overestimating how much processing power is needed to transcode. I bet that this configuration with a bare metal ubuntu server install and proper cooling for the CPU should be able to handle a 4k stream.
I run a 1045T at stock speeds with a plex server virtualized on two cores. That VM benchmarks almost exactly the same as this celeron (differences in architecture sure, but it should be close enough for a baseline comparison)
I recently downloaded star citizen 4k demo (48Mbps H264) for benchmark purposes. On that VM, I did a transcode down to 4Mbps and it almost played it back seamlessly. It's actually frustrating how close it is to realtime.
Point is, that is an extreme use case but given the score of this celeron, and using my example as a point of reference, it should be able to transcode that 4k video seamlessly or 2-3 lower bitrate videos fine. (Also keep in mind that running a baremetal OS will yield better results than my setup by slightly)
It's not an ideal setup but for the price, this ECS deal should be able to handle the smaller jobs.