Yes, that works and it's a nice upgrade -- I've done it myself. The early (hollow tube) center stands are prone to rust from the inside if they're missing the end caps, with unfortunate results.
You will lose the clunky, semi-useless automatic side stand retraction function.
Meantime, I have a question. If your side side stand is broken and your center stand is broken, what do you do with your bike when you're not riding it? Or are you just riding continuously, like Charlie on the MTA?