Selected answers from the Dumb SEO Questions G+ community.
Ranu Jain: No, it won't effect Google from crawling and indexing the new URLs that your redirecting to. ;
W.E. Jonk: Googlebot will follow and "discover" the re-directed URL. But since it is a 302 (temporarily) and not a 301 (permanent) redirect "search value" might not be passed (although over time Google might view the 302 as a 301). Furthermore what can happen with 302 is that the shortened URL will rank above or instead of the page .<br /><br /> (a little dated) ;
W.E. Jonk: From the expert panel in this weeks SEO Questions hangout on air on 00:09:01 into the YouTube video:
Robert Khayat: What I decided to do set up the analytics and webmaster through the short URLs along with a permanent redirect to the short URLs. Thank you so much for the answers it's nice to see a helpful community!