Can corporate tax loss carryforward function like a sort of insurance policy? I'm a graduate student in mathematics, with a casual knowledge of economics, so please let me know if this question is a non-sequitur or off base.

Here's the intuition I'm trying to capture: Suppose corporation A has a good year and makes a lot of profit, and corporation B, their competitor, has a bad year wherein they have a net loss. It seems that the following year, corporation B has a relative competitive advantage, in that they have a lower tax burden. 

In a system with no corporate tax—and thus no tax loss carryforward—it seems that corporation B wouldn't have this advantage which might give them some time to recover. In a system with a very high corporate tax, this benefit would be even greater.

Value judgments about the utility of a high corporate tax aside, is there anything to the idea that corporate taxes can serve as a sort of "insurance policy" wherein companies with a bad year are more likely to survive?
The structure of the tax ladder is such that the marginal tax rates keep increasing. The upshot is that if you earn more, your net earning (after taxes) will never be lower. So a company with a good year will always be better off compared to a company with a bad year, holding everything else equal. In this sense, tax does not provide advantage to companies with a bad year.

Your idea of "insurance policy" would be most closely related to the concept of automatic stabilizer. But this concept talks about the macro picture of the entire economy, so I'm not sure if it's wise to link the two together.