Architecture: net.connect() and connection callbacks ...

It'd be worth looking at how the existing ESP8266 library handles it because that has exactly the same issues and still works fine.

Did you see the inline documentation in network.h?

• for connect it's expected to block - but it doesn't matter too much if it doesn't since the actual HTTP callback won't be called until a header is received. The only case it'd really matter is in a standard (non-HTTP) connect call. If it turns out the connect has failed then send/recv can just return -1 when they're next called and everything will get cleaned up nicely.
  
• send/recv just return 0 if they can't return/take any data.
  
  

So it really shouldn't be very painful to make it work, with the minor issue that a simple TCP connect that fails will still call the connected callback. IMO that's something that you should look at doing after you've got working networking though.