The published 10.3 pre-release docs http://pro.arcgis.com/en/administering/system-requirements/arcobjects-sdk-system-requirements.htm mention every edition of VS 2013 except the Community Edition. I've got no reason to think that this edition would be excluded, but it would be nice to hear from someone who actually knows if it'll be supported when 10.3 ships.
Not sure if you're still wondering about this, but I was able to get the ArcObjects 10.3.1 install to pick up VS 2013 Community Edition.
From what I've seen, VS Community is the equivalent to express, but it removes some of the restrictions seen with express (i.e. it doesn't need to be installed for each individual platform and allows users to install extensions)
Freddie Gibson:
From what I've seen, VS Community is the equivalent to express, but it removes some of the restrictions seen with express (i.e. it doesn't need to be installed for each individual platform and allows users to install extensions)
My understanding was that VS Community was similar functionality to VS Professional but with licensing and MSDN restrictions, so should work with ArcObjects no problem. See Compare Visual Studio 2015 Offerings
Cheers,
Mike.