Hopefully the functionnalities of the application itself and the installer are unrelated, and you can test them in any order.
Edit: Answer to comment
Let me reformulate : hopefully the two assumptions :
1) My installer will put my user system in the proper state for my application to run
and
2) Provided the system is in the proper state, my application runs properly
are unrelated. Obviously, if your installer fails, your application won't work if installed by the installer :)
If you have doubts about that (and in particular are unsure about the definition of "proper state") that's probably the first thing you should test : what kind of "state" do you need for your application to run. Then you can test the installer and the application independantly