A wall under the marriage beam is almost certainly a load bearing wall. You would hear a difference in walls by tapping as the interior wall would not have insulation or anything else that would make it different than any other interior wall, except it's placement. Replacing the wall with posts and headers would work, but you need to set the posts to the same width as the walls. There are limits to how much free span you can have. Usually the front end of that kitchen wall leads into dining room, where the span is the width of the dining area. Then to to other half of the home, you will have just less than 12' (on a 24 wide) from the kitchen wall to the eave wall of the living room. Then usually at the hall end of the kitchen, there is usually a shorter open area. Point is, the ends of the kitchen walls support the free span areas.
Then you need to determine the size of posts and header and how they are to be attached. The structure of the wall (to be removed) gives it lateral strength. A 4x4 toenailed into a particle board floor will not be nearly as secure. I am not saying that this is your situation or plan. It is just that your plan needs to provide basically the same support as the existing wall.
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All information and advice given is for entertainment and informational purposes only. The person doing the work is solely responsible to insure that their work complies with their local building code and OSHA safety regulations.