Can a broken leg from a tube be soldered and used?

Are the broken pins used in the tube circuit? If not then no worries.

If they are and you want to try saving the tube I would insert the "repaired" tube into a tube socket saver. Then if the repaired pin breaks it would be stuck in the socket saver.
You could lose vacuum on the tube soldering on the pins? If so you get a nice light show at least.

The tube is not that expensive. About $50~70. If bought from Russia or Eastern Europe, $60 for 4 set and $25 for shipping.
What I will do is to find some tubes with long legs (at least 50% longer then 6C33C tube legs) and remove them from the tube. Then insert them into the 6C33C tube socket. Then you can connect the the pins and the tube's (with broken legs) legs with wires.
How does it sound?

Why not just by a new tube and use it? I know it sounds stupid to go through all these hassles, but I need to buy not one, but four matched set of tubes, and I've ran out of audio upgrade fund. LOL
Until I get a new matched quad set of tubes, I will try what I just said unless somebody yells me hard not to go for it due to potential hazard to the amp.

Ihcho, This is the first time I have heard the need expressed for matched sets of 6C33C. This is a tall order--particularly as these types have a relatively high failure rate during use, which further complicates consistent matching.

@$15-20 from Eastern Europe does it for me.

I once purchased matched pairs of 6C33Cs from BAT for use in my Atma-sphere amps. You might check with Victor Khomenko, if you live in the US. Any extra cost was well worth it, since the first set of tubes have lasted nearly 10 years with no failures and all still bias well. As to the repair job, yes I think it could be repaired and a proper solder joint is not going to break off in the socket. The bigger hazard is that heat from the solder gun could cause a fragile internal wire to go up in smoke, causing a short. I would opt to throw that tube away.