Unless the rescue image is specifically compiled for the distribution/version of the installed system this is not a good idea. Its good security practice to install distributir supplied patches when they are available - and maintaining a rescue disk which is an exact copy of the current state of your system would be a nightmare. Indeed, given the complications of this approach I doubt anyone would provide a rescue image capable of this.
The right way to fix the problem would be to boot up off the rescue image and restore the missing files from your backup. But presumably you don't have a backup since you're asking the question.
So that just leaves the option of reinstalling. But before you do that, boot up with your rescue disk and take a complete backup of the filesystem. Then when you reinstall, skip the formatting and use the existing partitions. Better yet, try to (major) upgrade to a newer version of the same distribution - this should preserve most of your config settings.
Then test everything and copy back any overwritten configs from your backup.