Is it safe to carry a metal tripod during the rain/thunderstorm
Having a collapsed tripod strapped to your bag is unlikely to be a problem. Holding an extended tripod over your head in the middle of an open field during a thunderstorm is definitely a bad idea. Then again, simply standing in an open field during a thunderstorm is also a bad idea. If there's lightning in the area, seek shelter immediately.
is it safer to just leave it and get to shelter ASAP?
It's safest to have enough situational awareness that you're not caught out in the open when lightning is a real danger. But things happen, and you should use your best judgement. If lightning is an immediate concern, run like crazy for the nearest building, car, etc., or make yourself very small. If that's the level of danger, I think my choice would be to leave the tripod, the camera, and anything else that might slow me down. But again, try not to let it come to that.
Assuming the tripod is struck, is it still usable?
Probably not. A lightning bolt can discharge up to 300,000 amps in a very short time -- that's 1000 times more juice than you get out of a medium sized welding machine. If you can even find the tripod after a direct hit, there's a good chance that it will have been scorched, melted, warped, and/or fused into something other than a functioning tripod.
On the other hand, it's not like the metal will have been poisoned by electricity. Have a look at it after the storm passes and it if still works, dry it off, fold it up, and put it back in your bag.
What I'm afraid of is if it might develop into a thunderstorm or related.
Don't let fear of a thunderstorm prevent you from taking a tripod on your trip. As discussed above, you should avoid putting yourself at risk for a lightning strike whether you have a tripod with you or not. Just keep an eye on the weather. If you hear thunder or see lightning, put your tripod away and seek shelter.