I think most of them should work, except for the Google based ones (Youtube, GoogleCast), you can try using micoG, but if you depend on these apps to work everyday, you will need GMS from Google.
But as soon as you (=your apps) use Google’s infrastructure … you depend on Google. One way or another. Most people cannot see this, because it’s the programmers making this “choice”, not them. And Google optimizes everything to “help” the programmers to choose their services. The “Google Play license check” as an example could make it impossible for you to use some paid apps, I fear. But I’m not an expert, maybe it will just work?
A good website to understand how the apps and the store work together is maybe http://blog.onyxbits.de/
“Please do not use Raccoon as a tool for piracy. Paid apps commonly perform license checks through the official Google Play app. Don’t buy apps that request the com.android.vending.CHECK_LICENSE permission unless you are willing and able to allow this.”
@paulakreuzer, @Stefan Could you please reopen the open os roadmap? It’s an interessting topic. Fairphone Open OS roadmap discussion