Probably. Depending on the app. Some applications are just App Store applications (or similar), that were or would be rejected. If it is one of those, extracting the .app file then codesign-ing the binary inside there should get it to work.
However, many Cydia apps require themselves to be installed to the "system" directory (/Applications), so won't work in the App Store/Developer directories, and also may require root access or access to other files that Apple would deny.
Your best bet, if you want to run one of these apps, is to jailbreak.