If it's a HA pair you should be able to do NDU. All LUNs in the HA pair are available on all ports in the HA pair , hence when you perform the takeover, partner system assumes responsibility for the failed system's LUNs without interruption. Only the 'session-oriented' services will be disrupted such as cifs, ndmp, http, ftp etc.. I suggest you run the Upgrade Advisor, it is an online tool, available on the NOW site, simplifies the process of planning Data ONTAP upgrades. It's not something that you should follow blindly, but it's a good starting point for your to begin the process.
I would recommend running upgrade advisor. I am not an expert on upgrades, but I can give you some pointers as to what you can do prior to running the upgrade.
Read the Release Notes as well as the Upgrade Guide of the Data ONTAP 7.3.7 for important information and technical detail before beginning your upgrade.
If you are running SnapDrive software on Windows hosts connected to this filer, check the comaptability with the upgrade os. If you are using SnapDrive with SnapManager for Exchange/SQL/Oracle/SAP/SharePoint/Domino, please check the compatibility between your SnapDrive and SnapManager before implementing the upgrade.
Before upgrading Data ONTAP, monitor CPU and disk utilization for 30 seconds by entering the following command at the console of each storage controller: sysstat -c 10 -x 3
Note: The values in the CPU and Disk Util columns are strongly recommended not to exceed 50% for all ten measurements reported. Ensure that no additional load is added to the storage system until the upgrade completes.
Make a back up of /etc/rc and /etc/hosts
Download perfstat and run it on a client as follows: perfstat -f filername -t 4 -i 5 > perfstatname.out
Save this output file for a couple of weeks after the upgrade is complete
Modify the storage failover policy to disable auto-giveback of storage. This is a NetApp best practice, to prevent automated fallback until the upgrade is confirmed to be successful.
Run - options autosupport.doit "starting_NDU 7.3.7"
This way you have configruration report before the upgrade, which could be handy when troubleshooting issues related to upgrade. I hope this helps.
As I said I am not an expert....but hope this helps.