Is latest 16" MacBook Pro powerful enough to stream 4k video from Plex to AppleTV without buffering issues? Scenario:

I have a mid-2015 MacBook Pro running 10.15.3. I've downloaded some 4k movies to that computer. They're in MKV form. I use a program called Plex to stream the movies from the MacBook to an AppleTV. Plex Server runs on the Mac and the Plex Client runs on the AppleTV. The AppleTV is connected to a 72" Sony OLED TV where I view the content. Both the Mac and the AppleTV are hardwired to the network via 1gb Ethernet. WiFi never comes into play. The 4k video quality is absolutely beautiful and audio is fantastic too.

Problem:

Once every five minutes or so the movie freezes. Plex shows a temporary error popup indicating that either the network is too slow or the CPU on the Plex server isn't powerful enough to convert the file. After a few seconds the error message disappears and the movie resumes at full quality.
The problem can be eliminated by telling the Plex client to play the content at 1080p instead of 4k but I much prefer the visual quality of 4k.

Question:

Will upgrading to the latest 2020-era 16" fully spec'd MacBook Pro (2TB SSD + 32GB RAM) eliminate the buffering issue when delivering 4k content from Plex Server to AppleTV? Is there a way for novice consumers like me to figure this out on their own by looking at the more modern Mac's specs? It feels like my current 2015 machine is almost powerful enough to do it, but not quite. I'm hoping a Mac upgrade would solve the problem.

UPDATE:

The CPU specs for my 2015 Mac are: 2.8 GHz Quad-Core Intel Core i7

The CPU specs for the current model Mac I'm considering for purchase are: 2.4GHz 8‑core Intel Core i9, Turbo Boost up to 5.0GHz, with 16MB shared L3 cache
I eventually ended up getting that new 2020 16" MacBook Pro and can conclusively say the answer is Yes.

4K .mkv files stream from the Plex Server running on the Mac to the Plex client running on an AppleTV box with no buffering/delays. This is over an Ethernet connection.