I don't recall seeing boiled eggs there. We were there in April this year. That is not to say that it can't be done, but you would need to ask first and I suggest doing so at least an hour before you plan to eat - or maybe at the beginning of the day and let them know at what time more or less you are planning on coming back to order your meal. Even if they can accommodate a special request, it really depends a lot on who you speak to and how busy it is.
You will still get the usual bacon, eggs, oatmeal, sausage and fruit. I am a fruit and yogurt person for breakfast and I used to pick up a fruit bowl every morning and just pay the $1.99 for the yogurt. I don't like pastry that much and especially not for breakfast so the ever popular croissant and danish option doesn't suit me.
By the way, I had never stayed at a value before and on the flight had a sudden panic about it ..... it was ABSOLUTELY FANTASTIC!!! We loved ASMu! The food court is also pretty good and we found the staff to be very accommodating and friendly.