You can sail with the Dowsar M dodger in place (up). If you compare the pictures of the M one above with the pictures posted of my Dowsar X version you can see why.
The Dowsar M dodger stops at the aft end of the cabin. This let's the traveler still function. You just remove the connector between the dodger and the bimini and you can sail with both in place.
The same is true of the Dowsar X enclosure I have (you can even go upwind with the sides in place and only the sunroof open for the mainsheet). There is a big difference in protection. because the M dodger has to stop short of the traveler you do not get full cockpit protection. The X dodger wraps around the front of the cockpit extending 18" back. This provides two completely protect seats at the front of the cockpit on the X. We never lower our dodger. It goes up at setup time and down when back on the trailer. (When we go out mastless we don't even put it down for trailering, we just zip out the front window.)
Here's the inside view
For both the X and the M dodgers (and full enclosures) you have to fold down the dodger and the bimini to lower the mast. The dodger does fit under the mast when it is in the storage position at the bow pulpit, but not when it is rolled back and attached to the mast step.
This brings up a mod I have thought about a number of times. I want to put a fixed 30" mast section at the step and raise the hinge point up. It would be just above where the gooseneck attaches. This would let you lower the mast and put it in the storage position without having to remove the boom, vang, boomkicker, mainsheet, etc. The mod would be designed so the aft mast roller was above the bimini. This would let you lower the mast with the covered mainsail/boom, dodger, bimini, full enclosure up and in place. It would save a lot of setup time.
Then I could switch from a soft dodger to a hard dodger with real windows and wipers, yet another follow on mod.