<<Disclaimer: Verify this information before applying it to your situation.>>

First off, I'd like to say that our family is between 3 weeks and 2 months into following both these diets simultaneously. 

We are under the supervision of our family physician. 
This is just to let everyone know that we're not jumping off cholesterol meds and diabetic meds without a Dr's supervision.
Obviously, I would like to remind people, that ANY diet that you choose to do, should be with the cooperation of your family's M.D.
The Atkins diet was actually suggested by our family M.D. when other cholesterol and Diabetes diets had failed.
For us, the weight loss was just an added benefit to trying to resolve the bigger health issues we were dealing with.
Just like a GF diet is not being followed for weight loss, neither is the Atkins diet for our family.

Our family's summarization (so far):
1 no longer dealing with hypoglycemia
1 has gotten off cholesterol meds
1 within 10 points of getting off cholesterol meds
1 is already in normal range for blood sugar (2 months ago was in hospital for having it over 300!) and will be going off diabetes meds shortly
1 (myself) has been able to get off meds for Pancreatic insufficiency (a very unexpected, but very much welcomed benefit to the Atkins diet)
Those who were craving carbs prior, are no longer craving them and have more energy
And of course, all have lost weight and/or inches

Summarization of emails I received:
16 people stated that they have done or are doing both diets with success.
3 stated that going Atkins helped with hypoglycemia
(Our family M.D. stated in his experience, people who are hypoglycemic that overdo on the carbs tend to become diabetic.)
2 stated that going Atkins actually helped for them to be diagnosed Celiac
2 stated that by going Atkins that they were able to get off insulin
2 stated that it wasn't a long term diet
(Perhaps these two were referring to an older vs. of the Atkins diet or weren't educated about it. The way our doctor has us following it, the Atkins diet is a lifetime diet.)
1 stated that it was really expensive
(obviously when you eat more meat and less breads it will cost more money... one down side that, for our family, doesn't outweigh the benefits)
Many people stated that it was easier to order in restaurants because most of the general population has heard of the Atkins diet as opposed to the Celiac/GF diet.

I did find, at least in the gerneral population... most people who are following/have followed the Atkins diet, don't really know what it's about. Most just cut back on carbs but don't actually follow the diet. So, if you choose to try the Atkins diet, PLEASE educate yourself first. Your success at any diet is obviously dependent on how well you follow it!

A big THANK YOU to all who responded!
Knowing ahead of time, that people had successfully followed both diets, gave me the encouragement I needed to dive into this more restricted eating lifestyle.
Now I am healthier, have more energy, and my life is no longer being directed by the medications I had to take! I'm free! Yay!

-K. McCullough

* Please remember some posters may be WHEAT-FREE, but not GLUTEN-FREE *