Hey if you can get away with it why not!!!
Don't expect to stay there long though. An expectation of J or F class crew is to address their customers by name, and the way they do that is to look at the passenger manifest. If your not listed, you're out!!
I know it's easy to do and they wont charge you the difference in fare, but i would be more worried about the embarrasment you will feel when they publicly escort you back to economy.
Did you ever see that Seinfeld episode when Elaine tried to do the same!! That curtain is there for a reason. It's a no go zone. Keep out!! You're not welcome, unless your name is on the boarding pass. Squatters are not welcome and you will be shamed!!