The writing suggests a different person and the physical behaviour the complete opposite. I think this could happen.

Hi Avy,
Yes I think this does happen, and not just when writing. In different contexts, when partaking in different activities, and especially when in different groups, we all adopt slightly different personae. In some cases the personae can appear significantly different from an outside perspective.

But what we have to remember is that all these personae are genuine aspects of one "real" person.

OK, I'm conveniently disregarding deliberate pretence/assumption of personae, but that's because, as belM implies, it's such hard work to maintain this kind of act that I think it's a relatively uncommon occurrence. More to the point, it's socially risky and, in the long term, probably not much fun!