Yes, you definitely don't want your oil leaking out b/c the bearings and shaft will be trashed at least and a seized bearing will destroy the pump housing. So it's definitely worth the time to make it right.
The empty of oil before filling, 10psi for 10 minute leak check is mandatory IMO, so you will know two of the three potential leak points are leak tight.
Potential leak points:
1) Fill plug threads
2) Pusher cone o-ring
3) Shaft lip seal
Any of these leaking will leave you with no oil in the pump and damage, so do the leak check for peace of mind and avoid wasting money.
Don't be surprised even if the leak check does pass with flying colors to find some small amount of water in the oil, that's why we change oil once or twice a season. The lip seal after several seasons wears a bit and will allow some water entry, once it gets bad the leak check will fail and/or you can replace the seal if you deem there's just too much oil loss.
A nice new tight lip seal often shows no water in the oil the first several seasons, money well spent driving a new replacement seal in there while the impeller is off and the shaft is out.
The shaft seal is a simple double lip seal, the garter spring goes to the inside and is in the oil bath.
Locktite 592 is specified for the fill plug threads, this one I've had surprisingly more leaks than I care to admit, twice in a row last year! I used another type of sealer b/c I had no 592 in my tool box and it leaked, quickly allowing water entry after the first use the oil was nearly 50% water seemed like but no damage was done fortunately.
As far as conversion, the newer jet pumps on 4-tecs were factory lubed using waterproof grease, like others have done for some time now, such as Yamaha. This works fine and the lube doesn't immediately wash away in the case of a leak also some have reported running with no cone this way. But still if water does enter, the pump has to be disassembled to remove the contaminated waterproof grease.
The conversion on those is to disassemble and remove the grease in favor of an oil refill. The benefit of an oil refill is it can easily be flushed if water enters, the downside is the oil can leak completely out in a short period of time.
On your pumps though, I'm not aware of anyone assembling with waterproof grease, although it might work fine.
Back in the day, we used to take this temporary shortcut of filling with grease in our old gearboxes that were worn out and leaky, and the antique gear boxes from the 40's and earlier were factory filled using waterproof grease before the lip seal designs were introduced.
So will it work in the case of your pump? I don't know but it might and probably will. I'm not sure I'd want to try though, considering if it didn't work the pump hub $$$ could be destroyed.
So replace seals and bearings as necessary, inspect the shaft for wear and replace any parts that are worn out, leak check and fill with gear oil. I think that's your best bet, IMHO
If your pumps are the plastic type, inspect carefully for cracks around the hub, the hub can wobble if several of the vanes are broken.