How much of a role tuition revenue plays in underwriting research?
Much of my answer here, holds in this case. It's basically impossible to tell. If a new professor gets a lighter teaching load in their first year, is that "underwriting research" even if the professor's nominal work distribution is 1/3rd teaching, 1/3rd research, and 1/3rd service/admin?  

Professors are paid to teach and research and serve internal university goals. How much they do each of those day to day is hard to tell. Now, that being said, if a professor fails to bring in grants to cover their summer months, I doubt many universities would indefinitely provide for them out of general funds.