If you use general software on the market, a copy protected cd would normally fail any attempt to be copied. The burn will most of the time be unsuccessful by failing at a certain percentage or freezing the PC. However, sometimes it will make a copy, leaving the protection out, rendering the backup useless as when it checks for the protection, and the protection is not there, the game or software will NOT run (unless in some cases emulated). CloneCD as well as some other RAW mastering burning software prevail in that they manage to copy the protection, as well as the contents of an original protected cd.
Your question:
Is it possible to throw the protection back in if a regular copy is made?
NO, however, there may be some hope with emulation.
Best solution:
Use a good program such as CloneCD, to read and write the original cd you have. CloneCD 4.2.0.2 had a bug with SD2.9, but you can use it in conjunction with FireBurner to make a working image. Just make an image using CloneCD and include a .cue file.
A program called DiscJuggler can also do this alone.
If you have latest CloneCD4.3.x.x then you should nt have a problem.
Further, you need to have a 2 sheep burner. What CDRW drive do you have?