Yes, but it might be complicated.
Basically, you need to decrypt the old update.upx to get the normal update.zip
Then you need to modify META-INF/com/google/android/updater-script
You need to edit the first line or two to eliminate the update newer than build constraint.
Then comes the problem with actually installing the modified update.
On my Poke3 I have a custom recovery that can install updates from a USB flash drive. It would be possible to make the same thing for Note 3 but it's pretty difficult if I don't own one and I have to do things by instruction over the net.
The problem without this is that /data is encrypted so you can't mount it (easily?).
Without /data you really have no place to put a 1.5 GB update.
You could use a USB flash and connect to ADB over WiFi and do it that way.
This sets ADB to use WiFi on port 5555. (Make sure you can access this before you switch. Although a reset should clear it back to USB.)
Code:
$ setprop service.adb.tcp.port 5555
I'm not saying that there aren't other ways to do this, but this is what I know.
If you are considering this and don't have one, order a USB Type C OTG adapter cable today.
Edit: For a second I thought that the Note 3 had A/B, it doesn't. If it did you could have just swapped slots and got your last version.