You should and I would not be surprised if you did not like it. The meat taste completely different to me, and not necessarily in a good way due to my life long acclimation to the industrial chicken meat we get from the store.
The eggs also taste different, much richer and a different color yolk from what I remember.
Can't reply in-line to the child post, but this is a cultural difference. In Europe, eggs aren't refrigerated at all, and they're not washed. In the US, eggs are washed and they're sold in chillers. The reasoning behind this: http://www.latimes.com/food/dailydish/la-dd-heres-why-we-nee...
Pretty sure the refrigeration is just for shelf life. Refrigerated eggs are good for months (even though the expiry date might lead you to believe otherwise).
I don't know about non-refrigerated but I would guess they can't be stored as long.
We get local pasture raised eggs every week from a co-op. You are correct in that they are different, they taste meatier, they are smaller and vary in size more, the yolks are darker yellow and they last much longer on the shelf.
Oh and they don't need to be refrigerated; and some of them still have chicken poop on them.
The eggs also taste different, much richer and a different color yolk from what I remember.