Here are my thoughts:
You aren't going to be able to share the files between the two systems because they are at different release levels.
The errdemon file is in the system's memory, so theoretically, it should continue working. But you can't be sure it will stay in memory, although since it is something that is constantly monitoring your system, AIX probably does keep it in memory. If that is the case, it will stay there and continue working until the system boots.
When the system boots, if you don't have the file replaced, you may receive an error because the /sbin/rc.boot file tries to start the errdemon, among many other things. (rc.boot is the third and final phase of the boot process and is invoked from the second line of your /etc/inittab.)
If the maintenance level of the system when you made the mksysb tape was the same as what your system is at now, I would think there would be no problem in restoring the errdemon file. Are you sure that is the only one that was deleted?
I would stop or kill the errdemon process, do the restore and then restart the process.
I have just performed a quick and dirty test on a sandbox here. I copied the errdmon file to another filesystem, then deleted it from /usr/lib. Then I forced an error by filling up a test filesystem. The error was logged. I copied the errdemon file to /usr/lib from the filesystem I had copied it to and restarted the demon (by typing /usr/lib/errdemon). Then I forced another error by filling up another test filesystem. It worked.
I think the important thing to do is to make sure the ML of the system on the mksysb tape is the same as what you have on the system now.
And, by the way, a force install isn't as bad as it sounds. You just have to tell AIX to go ahead and reinstall that particularl fileset even if it is the same or older than what is already on the system. Then, after the installation, you would have to reapply the ML to get that group of filesets up to the same level as the rest of the box.