Hi Kristin;
Welcome to Permies and Welcome to Rocket science!
Yes , absolutely in your case you can have a feed tube in the mud room and your barrel and mass in the other.
Popping into your mud room every 45-60 minutes to feed the
dragon will be no big deal.
My only concern would be your burn tunnel length. You cannot extend that burn tunnel roof beyond 10- 12" or so.
If you do, here's what will happen.
Your stove will work great! Dragon roaring, lots of heat , easy starting!
Part way thru winter your stove will seem sluggish....
Soon it will start acting up....
When you open up your cleanout ports you will find your pipes are more than 1/2 way plugged...
I speak from
experience here.
I thought it would be fine to have a long tunnel... (apx 15")
Turns out its a very bad idea. I learned all about doing a rebuild during a northern Montana winter... it can be done.
That J tube was in our uninsulated greenhouse/studio. I did a rebuild in about 3-4 hrs that day!
Much easier/less stressful to do a rebuild on a warm spring day!
So, if you follow build sizing parameter's closely and don't be like me and "modify them" you will be fine!
Tell us more (with pictures please) about your plans and about your home itself.