Yes, but then the vulnerability to corrosion and resultant splitting/spalling forces on the concrete at each end is not resolved. The stainless would likely be less likely to corrode (depending on steel spec and grade, and soil/exposure.
If the contractor did not weld in accordance with AWS D 1.4, then the welds are not structurally qualified. If the bars are ASTM A706 (weldable) rebar and were properly welded, then the simplest solution might be to excavate at least 3 inches below the bars, form sides with adequate cover around the bars, and pour a concrete strip along the length of bar to provide passivation and protection for the bars. Be sure the bars are clean, and the concrete is of good quality and properly consolidated.
If this is near a road which is salted, near a coast, or there are other reasons you expect severe corrosion, you could require stainless or epoxy-coated threaded bars. Not an endorsement of a brand (they are not a CRSI member), but DYWIDAG does sell epoxy-coated threaded bars, couplers, and accessories for soil nails and similar uses. Their couplings and nuts can be used as you describe (drill, through-bolt, and connect) and the epoxy-coated bars should work well even in corrosive exposures.