Thick pad carpets are tricky for robot vacuums.
It depends—mostly on your robot’s clearance and suction power.
A high-density foam pad adds height and softness. That means your carpet pile sits deeper, and a robot vacuum might get stuck—especially on transitions or when turning. Even if it doesn’t get stuck, a thick pad can reduce suction effectiveness because the brush can’t reach the base of the fibers.
Some higher-end robot vacuums (like Roborock or Roomba j-series) adjust power or have higher clearance, but I wouldn’t assume it’s fine. Measure your carpet + pad height. Most robots handle up to about 1 inch of pile. If yours is thicker or very plush, you might be better with a manual vacuum.
Check the specs before you buy. This is not a place to guess.