Probably not a good idea.

Here's what I do - it also lets me set up camp in two minutes in case of incoming storms.
I don't roll my deflated pad, I fold it accordion style into quarters.
I carry a lightweight daypack for hiking - and use it for tent and sleeping bag.
a. I put the tent poles into their sack and into the backpack first
b. Then I just stuff in my sleeping bag - adding a trash bag layer in case tent is wet
c. Finally, I top it off with the tent and fly - damp or not
Plus, it's really easy to pull out my tent mid-morning to dry in the sun.

I put the folded pad on my rack over both rear panniers.
Then I strap down the backpack on top.
It may look a little bigger - but it's lightweight.
And, as I said, it's really easy to get to if a storm is approaching.

Not the finest aerodynamics, but I'm not in the Tour de France, either.