Not on a Zones 1-6 Travelcard alone, because Luton is nearly 20 miles beyond the boundary of the Zones! The last station in Zone 6 is Elstree & Borehamwood, which EMR do not stop at.
If you held a Zones 1-6 Travelcard you could combine it with an Elstree (or Boundary Zone 6) to Luton ticket. This would be valid on EMR or Thameslink, including on non-stop trains.
You could also buy a Luton to Zones 1-6 Travelcard, which is effectively the above two printed as one ticket. Again, this would be valid on either operator, but if you buy it as a Day Travelcard and are doing a return journey from London to Luton, you would need to buy an additional single from Luton to Elstree/BZ6 for your way back.