Should phd candidates spend time on extra-curricular?
Whether or not you get a tenure-track job is going to be driven by your research credentials, and not by extra-curricular activities. However...


Interviews and job applications often ask about your service contributions; how you would go about managing people, budgets, and competing demands; etc. Extra-curricular activities such as student leadership may give you some concrete examples to draw on in addressing such questions. This is likely to result in a more compelling answer, which may help your overall application.
Your circumstances or preferences may evolve over the next few years, and you may not be able to find the right academic position when you graduate from your PhD. Participation in extra-curricular activities may help your CV when applying for non-academic jobs.
Networking is always helpful. You never know where you'll meet someone interesting or useful, even if it's just a fellow PhD student from a different department whose research connects to your own.
Variety is important. In my experience, it's good to have a reason to step away from your research regularly and think about something completely different. Often inspiration for difficult problems strikes when you're not actively thinking about them.