No, the main reasons to vote for or against an infrastructure project would be its utility (how many people would take it, what things it will enable, how many people would take it instead of a car or plane and the benefits that will bring), not how good it is at estimating costs.

But the budget and the cost estimate is used as the denominator in the utility justification function, so if it returns positive ROI at a certain cost, but cost overruns are 2-10x that, then it carries negative utility...