It would be a little darker, yes. I would test it first, since it might be a pretty subtle effect. If you have a pot with each value you could try them before purchasing the dual pot. See if you even hear the difference.

You could get close to the same effect with a 500K push pull pot by adding a 500K (or 470K as in the pic) resistor. All you would need to do is run the one leg of the resistor to the output leg of volume pot. Run the other leg of the resister to the left center contact on the switch. Run a wire to ground/earth from either the top or the bottom left contact on the switch, depending on whether you want the dark sound to be the up or the down position. That would be pretty close to the same effect as using a switch to go between the two gangs of the dual pot--and you wouldn't need a visible switch. It should sound exactly the same as the dual pot in 500K mode. With the volume all the way up, it would sound the same in 250K mode as well. The only difference would be that the taper would be a little flatter when you turn it down in 250K mode...All the same sounds you get with a normal taper would be there, just in a little different place than with standard taper.

The 500K pot with push pull would have another advantage. If the resistor trick does not get the sound dark enough for your tastes, you could swap it for a smaller value resistor (a 125K resistor would make a 500K pot equivalent to 100K)...or you could swap for a cap. Gretsch wires their mud switch with .012 or .039 caps I think. So you'd have more options to try.