Will it rust? maybe, maybe not...depends on a lot of factors

Having said that, mineral oil on your blade after each shave is about the cheapest insurance you'll ever find. The most expensive blade I have cost $140...mineral oil costs what, $0.001/use. That's cheap insurance.

Actually, I did the math. I've used about six ounces of oil liberally applied in the last year. That's $2.50/year for oil or $0.007/day based on 340 shaves a year.