Normally I carry my bike inside my car, but I've carried my carbon bike on a rack like that many times, and it's stored on a rack like that in my hallway. Neither of these racks have any clamping devices. I use 1" webbing to secure the frame to the car rack, and I run a bungy cord through the wheels and back to the rack to prevent vibration. In the house, I run a bungy through the frame, front wheel, and back to the frame to keep the front wheel from flopping. My hallway is not very big, and the bikes already take up too much space.

I once arrived at my destination 800 miles from home, went to take the bikes down and one of the front wheels was gone. Either someone stole it (?) or 800 miles of highway driving worked it loose and it ended up in the grill of an 18 wheeler. This was an old beater bike - not a wheel that would have been worth stealing. I'll never know what happened to it but fortunately was able to buy a new one and get it in in a few days, so my vacation wasn't totally ruined.

Just don't clamp anything tight on the top tube, or any other tube for that matter. You should be fine.

There is always going to be someone who will tell you whatever you are about to do is not a good idea. Good idea to listen, but evaluate the information and form your own opinions.