There's no reason they can't. The cards are marked as "noexec" in /etc/fstab because the FAT filesystem can't maintain the "executable" bit, so everything becomes executable.

If you remove "noexec", or format your cards as ext2 (for example) you can run code directly off the cards.

Also note there's nothing stopping an application storing data on the card if necessary (e.g. emulator disk images containing emulated programs).