is the membership worth it ?
Also depends on how serious
you are about your chess game but I mean - it's under $15 a month. That's cheaper than an oil change. I say give it a try and the worst that could happen is you are out a few dollars if you don't like it.
does membership "improve your game"?
no. absolutely not.
studying chess "improves your game" and it is up to you to figure out what kind of 'studying' works for you.
if you have a desire to get more access to the tactic trainer, chess mentor courses, or watch any of their vids. then you should upgrade the account.
I agree with thegreat_patzer. You have study and practice your game. Nothing is going to just be handed to you. You can pay for the additional perks of membership and based on the expertise here I would think it would be worth it but it is still entirely up to you to determine how extensive your work ethic is going to be. I am a pavement contractor in san antonio and it ties right in with my past experiences with chess and long distance running. You have to have the desire and willingness to put in the work. A 10X effort as Grant Cardone puts it, or settle for average. The fact you are inquiring about it already tells me you are hungry to succeed.
It gives you more access to tactics and lessons, at lower levels like mine they are super helpful. I think getting a member ship was worth it to me but not nessecaily for improving my chess (there are other tactic sites and lessons [YouTube]) I mostly got it to be able to play unlimited tournaments on here, you can grow quite a bit with or without one it really depends on what you think you need to get better