I'm so sorry, I dug in it again, and found that while drawing primitives in selection mode, they do not reach the rasterizer, but will be intercepted after clipping. I was sure that the selection is based on the depth of the fragment being written into the framebuffer, which, when the fragment is being rejected, would not get updated, which would make sense. But I was wrong.
So, what can you do about it:
You can still use alpha testing but you cannot use the selection mode anymore. This way, you lose the ability to identify objects, because you cannot assign names to them anymore. What you could do instead is color-code the objects.
So you assign to your pickable objects a unique color in RGB-space while rendering them and afterwards you have to read-back the framebuffer contents and check the color code.
The good news is that you can still use the projection matrix and viewport that you used in selection mode.
Since you are now really rendering something that you do not want to be visible to the user, you might want to use the framebuffer object extension to create youself a renderable texture to which you can render while doing the picking.