Is this a viable sentence?

It's viable. "I" expresses an inclination to curiosity to see that.

I don't think you can use the word "curious" like that. I feel like you have to say "I am curious" or "I was curious" or something similar. It would be better to say, "I'm curious about that. I'd like to see it."

“John claims his dog can jump 15 feet in the air.”
“I would be curious to see that.”

Your sentence is perfectly permissible. It just needs context.