No. Cutting your deployment time is equivalent to saving a one-off cost. A comprehensive set of automatic tests is a massive ongoing cost (it's by no means impossible for the tests to cost more than the product), forever. The latter vastly outweighs the former.

There are domains in which you need the tests anyway. If you're in one, you'll probably find your deployment cycle is also constrained by the nature of the domain. If it's not, and if the existence of the tests lets you deploy faster than you otherwise could have, well and good. But it certainly isn't worth investing in the tests just for faster deployment.