Are you shure that Google not index shortened urls? Please type on Google: site:bit.ly and you will see
Google indexed them but they are not showing as result. For ex- If you search hxxp://bit.ly/UCcW You will not find the above link in first 10 pages ( can't say in which page it is there).
Yes Humtuma that is correct,but if you have lot of shortened links which is in that shortened link,(who is pointed to your website) then people will find your website easily on Google and you will receive good amount of traffic.