That is about the last thing I would do. Columns and beam tied to the garage foot would be a yes but to tie the drive to the garage slab never. Expansion and contraction will tear both apart. Sit the drive on the beam with a bond breaker and let it float. Use an expansion joint between the garage slab and drive.Is your floor toothed in, perimeter of the slab 18" or so deep compared to 4" slab.
I would pour the approach similar to slab perimiter and pin it, (drill holes for rebar and install rebar to get them tied together), it will keep them on the same plane. I would taper the approach back 3 or 4 foot and score the concrete at that point to control crack, instal rebar through out the pad.