Regarding Google AdWords, it counts the actual landing page that the user (bot) ends up at. So if you are redirecting from 1 page to another on your domain, that is perfectly fine. Google AdWords accounts for CTR, relevance etc. (see more here: https://support.google.com/adwords/answer/2454010?hl=en).

This means that the QS will be calculated using the landing page after all redirects, just remember to keep the number of redirects to a minimum due to load time for the user.

Another thing, if you wanted to make an ad which pointed to a redirect which did not work, your ad would get disaproved. Google AdWords will surely keep you notified if your landing page is not working.

Like Highland is saying, most often a redirect is used to track a click from AdWords, if they want to collect additional data about their campaign.