From the various videos I have watched, using a pad in a hammock is not uncommon.  However, since a pad only provide insulation from below it is not going to be as effective as a bottom quilt which wraps the sides.

A typical foam pad has an R rating of 2 or less so I doubt it would provide sufficient insulation for 20F especially if there is any wind chill.  Generally when it gets that cold you want a pad with an R rating of 3 or more on the ground, 5 or more in the winter and I suspect you need a higher rating in a hammock.

My understanding is that most people find that hammocks run out of comfort at around freezing and while you can make them survivable below that most will prefer to switch to a tent if freezing temps are typical for the trip. 

I have no personal experience so take this with a pinch of salt.