It all depends. Every now and then I talk to a QF pilot on another forum and he gets first class all over the place on QF, so I'm not so sure that they don't upgrade their own employees. The airline I work for doesn't have an official policy on OA non-revs sitting in first, it is at the gate agents discretion. I always put jumpseaters and ZED/ID90 non-revs in first on our flights if a seat is open when I get to them on the standby list. Some people don't, but its just a power-trip. So even if it is okay for you to sit there, a bitchy gate agent can ruin everything. You're more likey to run into these kind of agents flying carriers that contract out their ground handling(like most int'l carriers in the US) to people who don't get flight benefits. They can't non-rev period so of course they don't see why you "deserve" an upgrade.
Even at airlines that do have policies not to upgrade OA employees, such as Air France/KLM, I know of people talking their way into first class or business. The exception would be really high-class airlines, such as Emirates, Singapore, and Cathay Pacific. Singapore actually has all business class A340-500s flying EWR-SIN and LAX-SIN non-stop and they do not allow non-revs on the flights, period. They are very strict on these rules. Here in the states, Virgin America is the only airline I can think of that absolutely will not allow any employees, even its own, in first class.
Another option that is more of a sure thing would be business class ZED tickets. Some airlines have these agreements with one-another where you can buy a more expensive ZED ticket that is for business class. You would have to ask around with your travel center to see if you have any. At Skywest, we do not, but mainline United has these options with a few airlines including Lufthansa. Seeing as we use Delta's ZED agreements, I'm assuming they don't have any either, but maybe Mr. Taylor can confirm.