Can table columns with a Foreign Key be NULL?

I have a table which has several ID columns to other tables. I want a foreign key to force integrity **only** if I put data in there. If I do an update at a later time to populate that column, then it should also check the constraint. (This is likely database server dependant, I'm using MySQL & InnoDB table type) I believe this is a reasonable expectation, but correct me if I am wrong.