Allowing degreaser to dry on a part is a bit extreme. For most people that scenario is never to going to come up. A more realistic scenario is rinsing things off and just not doing a great job. In this scenario there's no long-term damage done but it could mean a lack of lubrication.
Degreaser is specifically designed to break down the lubrication your bike uses. The whole point of this article is to help you find the right product to get your chain lube off the chain. If you haven't done a great job rinsing it off, the new chain lube won't be able to properly adhere. Just make sure you do a good job getting the cleaner off before applying new chain lube.