Yes you can wire it this way. I prefer a separate switch as I can then pre-lube the engine when I want to not when you turn on the kill switch.
It does mean that you have to remember to flip the switch for it each time you start and stop the engine so there's that, but I had mine wired the way you asked about and changed it to it's own switch later.
This in on a non-Lemons race car so I'm the only one who drives this car in races.
The only time you really should need one at all is if your car can corner at a very high rate of "G's" and that takes "sticky" tires and Lemons doesn't allow anything that sticky. A properly modified oil pan usually is all that's needed.
I modified a number of Lemons cars oil pans and none of them ever lost an engine due to loss of oil pressure. Head gaskest, yes but no failure due to oil starvation and one of these cars was a top ten car and two time class B winner!