How to test cut-off valve

[2003Boxster]

This is the cut-off valve of the secondary air injection system. I suspect it is malfunctioning and that is why my AOS is about to give up (replaced 7K miles ago).

2003 Boxster, 2.7H
- AOS soon to be replaced twice in a year (see next)
- smoke at start up with increasing frequency, say 2 out of 10 times. It goes away after a few seconds
- I did find oil in the vent hose of the AOS and in intake manifold so the AOS is toasted but I do not believe replacing it is enough, the problem is coming from somewhere else and I suspect a stuck cut-off valve.

Questions
1) is the cut off valve open or close when the engine is off? I try blowing in it and it is definitely close
2) how do I test if it is working?

Thanks!!!

BUMP: added the poll, cool idea, I did not know we had it!