It is absolutely possible for a thermocouple to "die slowly" where it will work intermittently for a pretty long time. But, what makes you think it's the thermocouple? Granted, that is a pretty common failure point in gas fired units, you don't mention anything that actually points to a thermocouple failure (or really, any specific component) as a possible culprit.
If you are really convinced that the thermocouple is causing the pilot to turn off, you can try rubbing it with some sand paper or one of those green 3M scrubbers. You want to take off any rust/corrosion/crud and get it as smooth and shiny as possible. Use the finest grit sandpaper you can find. If you do this and it fixes the problem, it's still very likely that it will come back within a few weeks, although you might get lucky and have it come out more or less as "permanently" fixed.
You really do need a multimeter to properly test it though. I found some instructions (which I will not link to) detailing how to "test" a thermocouple with a paperclip, which just seems like a bad idea.... please don't do that.
Personally, I would try the sandpaper first and see what happens, and maybe spend the $15 on a cheap multimeter (or borrow one from a friend). If you are in an area that is already getting very cold, you might not want to risk it. In that case, the TC is usually a reasonable bet. Good luck!