Does it make sense to use an online ELO-rating-test for a beginner as a monthly test tool in order to see my progress? I'm almost a beginner in the chess world who at the moment only plays online and watch various chess lectures on youtube.

I'm thinking about using http://www.elometer.net/ 
on a monthly basis in order to see my progress over time.

What are the pro and cons of doing that?
Well, the main problem with these tests is that they aren't reliable. They can only give you a rough indication of your playing strength, nothing more. Maybe something accurate to 100 rating points, and it's very hard to gain 100 points in a month, even for a beginner. So it will be hard to measure your progress on that scale.

Also, taking the same test over and over again makes you recognize certain test questions, instead of solving them with pure chess skills. And lastly, they measure your ability to solve chess diagrams, instead of your playing strength. That encompasses many more things like an opening repertoire, knowing how to spend your time over the game, etc.