Nope. When the phone is set up, it has a unique identifier (which you can't see) and when you install apps to the SD card, it links them to that unique identifier. If you hard reset or flash your phone, that identifier will change and the apps on the SD card will no longer be linked. If it detects apps after this it will tell you they can't be used and must be deleted. Mainly to stop people installing apps to their SD card, letting their friend borrow the card and they copy the app/game to their phone, getting expensive apps or games for nothing.
But your apps will be up there to download again as that's stored in your purchase history.