If you plan on using a nail gun...don't turn into a 'gun slinger' (swiss cheesing the top plate to the main carrying beam structure)....and you should be alright...
As mentioned already by Jproffer, you should have zero problems...it's done all the time in basement remodels. You could use 2 x 6's to build that wall in order to hide the posts inside the walls, just take into consideration the thickness of your carrying beam as well. What I mean is that you may want to build that out also, in order to meet the same 5 1/2" depth of your framed wall. That is usually how we tie them all in together.
Example of the concept: Lally column mounting plates usually extend 'past' the underside depth of carrying beams. We usually build the sides and undersides of the beam itself out with strapping, so that the upper mounting plates do not protrude out,. They are hidden in order to get a 'seamless' look to the 'finished' beam. (no multiple corners or edges - just straight clean lines)