Sealing the drywall at this intersection is a good thing, if its done at the right time.

The simplest way, is to gasket it prior to hanging drywall,

(note: Denarco gasketing on the bottom plate of the ouside/insulated wall)

Sealing it now, would be a tedious thing to do, if you are in fact wanting to seal the drywall to the bottom plate, (which would stop air infiltration from the stud cavity into the conditioned space) The dust you allude to, is insulation dust that rides along with the air movement.

I dont think that sealing this, would significantly reduce the amount of dusting you will need to do.

Most dust that enters a house thru air leakage, comes thru the ceiling/attic plane, where air movement and gravity facilitate it entering the conditioned space.

Non air tight recessed cans are the most noted offender.

Sealing the bottom plate to the floor sheating is quick easy to do, even if the drywall is hung. While this will eliminate some air leakage, it wont stop much dust, per se, because there isnt much dust that would enter at this point.