Is this specific way of notating meterless music possible in MuseScore ?

My guess is that you can notate this way, but I don't think you'll get playback. You'll probably need to create the music normally, then hide/delete stuff you don't want to show. You can probably find a symbol for your seconds mark in the master symbol pallet.

Try writing a custom time signature of, say, 120/4. Then you would know that (at least for the default tempo) that a measure takes one minute. You could then put in staff text markings to signify increments of time. Your jpg looks like it is implicitly metered. The problem is with having note shapes that imply time. It seems like you would want to have only shapes for pitches. The next step is maybe a bigger problem. i am not sure the program can stretch distances between notes to approximate the real time markers.

You sure can get sufficiently close without too much fiddling around:

You'll want to turn on invisible things to see most of what I did. The main thing was starting from 4/4 (although 3/8 might've been easier in hindsight) and removing the remaining beats per measure; making each measure match up with a seconds indicator of duration.