Without understanding any more deeply, I would activate a smartphone (for myself) without using nor entering a google account. I do have a google account, but I would not put it into the activation of the prospective smartphone. The purpose for the smartphone would be cellular phone voice calls, text messages, maybe email using Yahoo and AOL, maybe voicemail, internet searchs and browsing such as for using the google maps site. For internet purposes, I would use wifi when available, and the cellular plan's data service otherwise.
Maybe something can be said regarding my use of "should" in the question.
No intention yet decided about looking for or downloading & installing any "apps". I would assume what I would need is already built in to the smartphone.
Now I have the impression that a person SHOULD register a separate gmail/google account dedicated specifically for the use of the smartphone - but I just do not like the idea that some big mysterious organization will have more of my personal information; just another identity protection risk. The cellular service airtime provider would already be given that information.
I wonder how my data is used if activating the smartphone with including a google account. Is any of it, like my name, displayed from my google account when someone receives a phone(cellular) call from me? Maybe I want it displayed, or maybe I do not want it to be displayed.