Would participating in student politics as a PhD student without an advisor create a bad impression?
It very much depends on the quality of your PhD work. If that looks good, it can be a boost to your CV. However, if your work is middling, this may appear like escapism (or perhaps a political career is what you should pursue instead of a PhD).

This is always, as @user3209815 said, your decision. What is unlikely to work well is to take up this job and getting even further behind on your PhD work.