Unpack the *.deb file containing the modification to see in what form the module is distributed. Also have a look at the content of the other package and see what files are shipped there. If some files are precompiled modules for a specific kernel version (*.ko files), then those modules will almost certainly fail to cooperate with a more recent kernel, and updating Ubuntu without updating the kernel is asking for trouble as well.

If, on the other hand, the kernel modules are distributed in a source format (*.c), perhaps containing some binary blob, then the deb package will likely use dkms or similar to have modules compiled for the current kernel, and the shell script might do some compilation for the current kernel as well. In those cases, you should see whether the modules do compile against the sources of a current Ubuntu kernel. You should be able to compile them on a test system, not using the target hardware just yet.

If they do compile successfully, chances are good that they will run as intended, although there are of course no guarantees. If they fail to compile, you can see whether you can locate a kernel version recent enough to support an upgrade but still old enough to be compatible with those modules. Or you could adjust the module sources to take kernel API changes into account.