As far as logging off is concerned I do not bother making any special effort. I just log out. It seems likely that there is a horde of insignificant people (not shown) who are constantly moving around town so on disconnect you can assume I got lost in a sea of faces. In the wilderness you can assume there is a suitable amount of vegetable and mineral obstructions into which I have disappeared. This is just my take on what is essentially role playing an OOC event.
As you were, soldiers 
Agreed. It depends on who's around you. If you're in the company of people who are "hardcore" about staying in character, then you might move your character before signing off. Otherwise, it doesn't really matter.