Fasten a pair of foam cups together at their wide ends and roll them along a pair

Question:

Fasten a pair of foam cups together at their wide ends and roll them along a pair of meter sticks that simulate railroad tracks. Note how they self-correct whenever their path departs from the center. Question: If you taped the cups together at their narrow ends, so they tapered oppositely as shown, would the pair of cups self-correct or self-destruct when rolling slightly off center?