Is it a breach of protocol to contact people higher in the academic hierarchy for social reasons?
It is great that you are thinking about networking as a PhD student. 

My advice would be escalate the relationship by one step. Going from a "nice" conversation at a previous conference (where no email or contract info was exchanged) to a social activity outside of a conference is a bit like asking someone you had a coffee with once to go on a trip with you. It escalates the relationship very quickly and could get awkward. Furthermore, many people don't stay extra days at conference locations so it is likely to be unsuccessful.

Less intense ways to connect:


Send them an email saying that you noticed they were presenting at the conference, and you are looking forward to seeing their work and chatting again
Run into them at the conference (as Ian_Fin suggested) and ask what they are doing for dinner or lunch on a conference day