This might sound like a dumb question but...

Lets say you have a standard pop song or rock ballad in E minor. Would it ever be a good idea to use E dorian over the E minor chord when playing a lead? Or would it be best to just stick with E minor and E minor pent. Is it because the mood and melody of the song is already firmly established and using E dorian over the E chord will sound out of place or is it a just dissonant thing?

If I just played the diatonic c note from E minor I will have more tension than the c# from E dorian right?
It's in E minor, which is not modal.You can't be using E dorian, in this case you would just be using the E minor scale with a raised 6th acting as an accidental.