If it is a prized possession then obviously a little padding under the bike would be nice. Also, pedals aren't meant to take much side load abuse, so resting your tandem on them and bouncing down the road would not be a good thing for the pedal bearings. Resting on the pedals also creates a stress point on the end of your crank arms which are built more for rotational loads and not hammer hits from the side.

When we travel in our motorhome, we slide our Calfee into the bays underneath. I do remove the non-drive pedals, and captain's seatpost w/stoker bars, and obviously remove the front wheel too. Plus I place some deep foam under the rear triangle & crank arm and a protective cover over the front bars/shifters. Front wheel goes into a wheel bag. This process takes me less than 10 minutes to store or remove and setup. FWIW, I do the same with our singles.

We have always preferred to travel with bikes inside our vehicles rather than exterior racks.