Is it proper to have an informal relationship with your Ph.D supervisor(s)? Can this be an advantage or a disadvantage? And can this relationship create the desire academic intellectualism or otherwise?
There are always pros and cons for every decision being made. It is very hard to make any conclusion as it depends on case-by-case basis. It is totally based on the mutual interaction between the researcher and the supervisor.
I don't know whether an informal relationship is proper or not, by my major professor and I were the only two guys in the business school that played golf. We teamed up and played in about 20 team events per season. It was an advantage for me because my share of our winnings kept me in new clothes, and later we placed a couple of papers in very good journals.
your Ph.D. supervisor role is to guide you towards becoming a scholar and researcher. It’s good to be on friendly terms with him. However, being overly friendly and informal can be a problem later on in case have a disagreement. it will be hard for you later on to tell him that something is wrong/needs to change without damaging the relationship, and perhaps your professional opportunities.
I'm not sure what you mean by informal relationship, do you mean seeing this person as a mentor or perhaps building a personal relationship that could lead to friendship? I don't see why not, if you and your supervisor get along, then you get along and will likely stay in touch after you finish your degree. @Mohammad Assi is right about sometimes being too friendly and being afraid to have a disagreement. However, everyone should have the skills to resolve conflict (where it can be resolved) and not be afraid to tell someone that they are wrong, if you truly have a good relationship with the person then they shouldn't take your disagreement or criticism personally, but with stride.