Well, I would suggest you yes. Syncing google calendar to your phone is a nice idea. Because our phone is with us most of the time so syncing it will remind us immediately and easily of the important dates we should remember and the tasks or activities we have during that day.
Furthermore, syncing other apps of our phone in our google account is an ideal one. Because I lost my phone once and I forgot to sync my apps to my google account so there is no other way now for no to retrive what I have in my lost phone.