Yes - pressure can give a nudge. I tend to write more songs just before a 'sing your own songs' session is due. For me I think it just reminds me to capture something instead of letting it slide past a a transient thought.
A friend of mine has been asked to write a song about rivers for some agency which has to do with rivers & stuff. He can't seem to do it no matter how hard he tries. He's got the music but not the words at the moment. So I think the pressure is definitely not helping him - maybe its too specific a task to allow him to slip into creative mode?

Kris