I think it depends on the nature of the startup, but I'm not qualified to answer that sadly. If it is in the IT, I think you'll have an easier time perhaps? http://www.thelocal.dk/20141206/how-to-get-hired-at-a-copenhagen-startup This article might give a little insight though - The article has a sector on 'Do I need to speak Danish'
Every Dane below the age of 60 generally speaks English, so don't be afraid of the local language barrier
In regards to social life, there shouldn't be any issues either. In my experience, if there is a person in a group whom do not speak Danish, we all just start speaking English instead. If anything, it's a nice conversation opener, we are always interested in where people come from, so that'll always get a conversation flowing.
I found this article after browsing around for a little, and it might be useful. I have a different view from hers, but that might be due to being in a student enviroment.