Not that I'm aware of. So far I’ve never came across any evidence showing AdWords is connected to regular Google Search from any scoring perspective. I just use my own logics and believe (to a degree) that AdWords would not (at least) go against its sister.
Although not our business, you would help us answer your question better if you tell us why you’re changing domain name.
Were you unsuccessful with the old one so you hope to do it better with the new one?
…or you simply found better name for your site?
Anyway, when you change the domain name, you want to keep your site’s ranking and indexing history, whatever they are, unless you have a specific reason for wanting your OLD site (old domain name) disappear from results.
So, if all ok, you definitely want to implement 301 which means “I moved”. That way, all bots will rewrite their indexes with new site’s URLs.
I am saying all this just to make you aware that with 301, there should be no doubt about duplicated content.
You can actually hurt your new site with not having 301.
301 is the only right way of doing it.
Again, if you are trying to delete the history of your old site (domain name) and hoping that Google will not connect the new one to it, that’s another story.
In regards of index, without 301, it may happen that your old pages never get properly deleted – or stay indexed for long time.