first thing, before you stain, I will assume that you will do a fine finishing job and sand in the direction of the grain. this will make for a nicer stain job. Then be sure to use a good sand sealer or wood conditioner before staining so that the stain is uniform all over the project. Stain in the direction of the grain.
Now the cabinet deal. I am not sure where he/she is coming from on this statement. If the wood is still green which I know its not, the wicking of the moisture would allow the drawers to work better as the wood will actually shrink. Since we know that the wood is dry, then the sealing of inside and outside of drawers would cease any moisture soaking in and as you say, seal it. When I cut doors off at the base to accomodate for higher new carpet, I seal that fresh cut so that expansion does not occure from wicking of moisture.
If you seal it, I would not get any stuff on the actual glides or runners, but sealing it seems to me to be a good idea.