Rinsing is a waste of good soap.
I rinse the outside of the jar so it doesn't get scummy, but it's pointless to rinse the inside.
As you get more experienced, you will make much less of mess with the soap (as long as you don't lather on the soap). All you'll be left with is the brush marks on the soap and it's not worth rinsing it off.
Crap, without even thinking today I put the lid on my soap and put it away before it dried.
Will it be OK if I take if off to dry after work?
Yes -- it will be OK.
Remember, this is only shaving, not brain science . . . .