Yes, so long as the searcher can't ever go back to a "passed" company. But in reality, a searcher can go back to a company she initially passed on (although sometimes the company will get snapped up by another buyer, the seller will be annoyed by the delay, etc.). Still, the secretary problem is a useful mental model even if it provides no optimal solution for searching: it's not a bad idea to start your search by contacting a handful of random targets just to get an idea of average quality (e.g. a initially sampling from 4 target industries in a broad geo range rather than just contacting the plastics manufacturers in the Nashville metro area).

I'd argue that the secretary problem, which is also called the marriage problem, applies more strongly to dating and marriage. I've told my girlfriend that she's beats the first 37% of girlfriend/dating candidates I've dated which, given she majored in economics, she both enjoyed and rolled her eyes at. Your mileage may vary with your significant other!