Yes, but you would need to address venting. So not so fast. Make sure the smell appears in the sink bowls. If the smell turns out to be more under the sink or from the dishwasher, reorganizing the drain pipes would not help.
EDIT: Looking back it looks like the line I thought was a dry vent was actually that cleanout next to the cold supply.
If I were to suggest something that would work, it would involve adding an AAV for venting. Ontario wants AAVs to be 6 inches or more above the flood level of the sink. But if you were to put the AAV under the sink, which is the common way in the US, it would work well. Again, make sure the smell is from the sink bowls, rather than from the dishwasher or a dead animal in the wall.