Yes to the out of the shell. I have tried to do it without, but haven't been able to remove the shell without thawing first. I will tell you that they didn't crack when frozen, so it may be that it would work without cracking them into a bag. I just haven't gotten that far yet. My test set were some old eggs that I didn't plan on eating.
I had also planned to crack them into ice cube trays, freezing and then putting into a baggie. But I just kept putting it off. So when I did it, I just wanted to get it done. Since then I have just done it this way.
And yest the perfect protein.
You could always cook them up and mix them in the chicken mash a couple of times a week also.