Are sensitive teeth more prone to cavities than unsensitive ones?

Indirectly yes: Because one tends not to brush / maintain proper oral hygiene due to the sensitivity - ones rushes through the sequence without giving the attention it deserves. Sensitivity can also be the result of gum recession - roots being exposed and can lead to root caries. Best to be seen by a dentist for a comprehensive exam / treatment recommendations. Hope this helps.

Generally, No: Sensitive teeth can be due to exposed roots (gum recession), roots are more prone to decay as they lack the enamel layer that is strong. Beyond that, no more prone to cavities than other teeth. Brush, floss, fluoride: best you can do. See your dentist regularly.