Answer:
Yes, you can pick a simple lock in either the unlocked or locked position. There isn't much difference in the actions between the two.
Additional Response:
When a lock is unlocked, there are no more pins to manipulate. All one has to do is turn the cylinder inside the kik (Key in Knob) housing, and it slides into place. You can use a pick, you can use a fingernail file, you can use pressure on the outside of the actual cylinder and just turn it with your finger.
An unlocked cylinder - in all cases that I am aware of at least - has the pins separated and the bottom pins aren't even touching the kik. There's no resistance present, so yes, it can be "relocked" with a pick. It can also be relocked by putting your finger on it and spinning it a little bit.
There are no pins to manipulate in order to "relock" any lock I have ever encountered - and I've seen quite a few.