That should work with the following big caveat: if you were on the MJ7 kernel (or earlier), and the new phone is on MJE, restoring the full nandroid backup probably won't work at all and is not adviseable. (Remember that Safestrap "ROM"s do not replace the stock kernel).
If the two phones are from the identical release, then what I would do is the following:
- Root and install SafeStrap as usual.
- Immediately make a Nandroid of the Stock Slot using Safestrap. Get it copied off the phone someplace safe (and named in a way that you can remember it) too.
- Make a second slot in Safestrap and restore the backup from the previous phone to this alternate/second slot.
( Note if you were using a ton of the userdata partition on the old phone you will need to right-size the 2nd slot when you create it. Of course, if you were a data-pig on the old phone and there is no room for a sufficiently-large 2nd slot, then this method of rescue is not available to you. In this case you could restore the original nandroid backup directly to the stock slot - only if you were 100% positive of the same kernel release being used on both phones - but if something goes wrong here you might be making a trip to Odin to re-flash stock and then going through the rooting process all over again ).
- You can use it this way for a little while if you like to see if things are working, or rescue critical data from individual apps, or perhaps make TiBu backups of individual apps (that can be later restored into a different ROM). If things seem to be going swimmingly, you can certainly repeat this process, restoring to the stock slot and then destroying the alternate/second slot.
Note that there are other means of rescue of individual apps which do not require a full restore; this is because the Nandroid backups are (concatenated) "tar" archives, and with sufficient command-line knowledge, you could manually splice into place the appropriate folders from /data/data/*, /data/app/*, and /data/lib/* for individual market apps you wanted to rescue from the old backups. Essentially you are doing the same thing that TiBu does, but manually using adb with the phone in Safestrap recovery mode and the command line.
I'm not going to document this, as it is too tedious to do so - either you already have the working knowledge to do this or you don't. The only tricky part to it is getting the user/group ownership of the files correct. (The easiest way to do this is to install the app from the market, then record the owner/group information it used for the new install of the app, restore the /data/data/* files into the correct place, and then as root "chown" them to the correct user ID... either that or run the "Fix Permissions" script of the recovery).