The vast majority of OEM saildrive installations just use the molded hose from the saildrive to the sea water pump without any strainer, and the saildrive water supply slots function as a strainer. This functions adequately in most situations. You could, however, install a strainer between the saildrive water outlet and the pump inlet, or you could forget the saildrive pickup altogether and use the existing thru hull
fitting and strainer.
My personal recommendation (after 30+ years of VP employment) would be to use the existing thru hull
and strainer. Mix up some filled epoxy
putty and fill the water pick up slots in the drive leg and also the water pickup up hole in the bottom of the drive. Give the cured epoxy
a coat of barrier coat and bottom paint
the leg with a suitable paint
. Close off the water valve on the inside of the boat and forget about it. The reason I recommend this is that shell growth can occur within the water passages of the drive and it can be a pain to clean out.
Your idea about placing a "T" in the seawater hose between the pump and the HE and using that as a vacuum break is fine. It will give you a visual indication of pump operation and also avoid the potential problem of vacuum valve salting up and sticking closed. Try to run the hose such that there are no sags or dips that may retain water after the engine shuts down.