That sounds like it will work. Usually you attach the column to the wall with a bracket from Simpson Strong-Tie - Helping to Build Stronger, Safer Structures.
Since you posted this question, I would like to breach a good subject.
A bit more advice I will give is this, if you have not already, get a permit, and possibly an engineer to look at what you are doing. I know it is a Pain in the pocket, and you may be afraid of the department in your area. Most folks are., some for good reason too.
However I am going to share a short little story. A couple recently finished a beautiful master bathroom remodel on their home. They pulled no permits and had done the work themselves. They knew enough to get the job done.
One week later a pipe froze , and leaked water all night long down through more floors of the home, below was the kitchen. You know how bad this story ends. The really bad part is the insurance Co will not cover anything. That means , no cleanup of the water, damaged cabinets, buckling wood floors, finished basement ceilings, kitchen ceilings....you get the drift.
I would hate to have something happen to folks out there when they do not CYA. Insurance CO's are getting tougher, and I am afraid it will only go downhill from here.
Good luck on your project, it sounds nice. Sorry for the soapbox, just trying to help out.