Naah, that's not the effective radius

. Not for measuring the circumference. Although the circumference shrinks a little, like 2mbb said, it still has to cover the whole circumference (minus the little bit of shrink) of the 360 degrees of tire. Compare it with the track of a tank. If you would move half of the guiding wheels upwards, so you would get a kind of square, you still drive the same distance with one cycle of the track. The same with your tire. Just try it out

. Deflate your tire 30% and measure the circumference. You will see that it doesn't differ much with the inflated tire.
About the axle and the deformed tire, 2mbb: Your explanation would be right if you would fold the ... of the tire (don't know the word - anyway, the part of the tire that touches the street). Because then the circumference would be smaller.