As I am a beginner (second year playing....first REAL year) I will put in my experience with this matter.
Last year I played maybe 4 times all year and really liked playing but was terrible. I would keep score every round, and would get the occasional 1, 2, or 3 over on a hole and would be psyched.
This year, I have played at least once a week and have kept scores every time. I signed up for oobgolf and have been putting my scores in there now. It is really cool to see the progression over the last couple months. Looking back on it, I wish I had done this from the beginning, or at least all this year!
So long story short, for me, keeping score has been good and I wish I had actually been better at it. I recommend signing up for a place like oobgolf so once you really get addicted you can look at it and hopefully see that you improved.