A:Answer The quick answer is yes, but with possible caveats.
The monitor should, by all accounts, be able to play 1080p signals via HDMI. My specific model does not do that. Any 1080p signal (or resolution close to 1080p), exhibits behavior similar to a bad connection (black screens, frame dropouts, visual artifacts). This is true whether a Nintendo Switch (in docked mode) is driving the signal or a desktop GPU (I used a RTX2080 SUPER for my tests). After about a month of testing with 6 separate HDMI cables, a separate Nintendo Switch dock, and using a desktop GPU for further testing, I found that the monitor (or at the very least my specific model), has issues with HDMI inputs at resolutions around 1080p. If one drives the monitor with resolutions at 720p or less OR resolutions closer to the native resolution of 3840x1600, the monitor will have no issue displaying those resolutions via HDMI. So, on the HDMI input, if I set my Nintendo Switch to display 720p, it works flawlessly, but as soon as the 1080p setting is used, the monitor will exhibit the above issues. I expect an EDID issue on HDMI.
The displayport implementation works flawlessly at any resolution, so I currently have a converter setup for my Nintendo Switch which lets me connect it to displayport whenever I want to play it at 1080p.
Now it could be that just my specific monitor is effected by this issue, but just be aware that it is something that one user(myself) has encountered.