2003 cluster - so it's a Wintel box, right?
I haven't heard of such thing - NetBackup upgrade will stop NetBackup services, and that means the clustered resource for NetBackup will go down, yes.
If you see other clustered resources going down too, or the cluster fails over, then probably you'd need to check the dependencies configuration on your cluster - possibly (my wild guess here) other resources depend on NetBackup, or the whole cluster is configured to fail over if NetBackup resource fails?
Well if you are in a position to affort a "test" then do it again and check the installation(upgrade) progress log in the %TEMP% directory.
Also, if you have that many servers, you should have NetBackup support contract - call Symantec, you are paying them for support, so get support out of them.
If you are not sure about support contract detail, you can still give it a try - once you call them, give them the location/address of your server / datacentre, they can find out if you have a support contract or not.
:-)
Abe