You could, but I wouldn't advise it for two basic reasons.

First, cycling shorts are designed to be worn when you are sitting down and half bent over. They don't do well when you are standing up.

Second is a matter of health and hygiene. Perspiration is going to build up in the pad instead of wicking away. You end up with a nasty case of jock rash. Not pretty.

While equipment can get expensive, I'd still suggest using sport-specific clothing in this case.