Emboidery on a quilt???
 

How does a pretty dense and stiff machine embroidery design work on a quilt? Is it awkward and stiff? I plan on putting two layers of batting in mine?

Yep, it's still stiff, and washing will not soften it, and it will probably bunch up when laundered. You will want to use a poly batting that's not going to shrink at all, and pre wash your fabric.
If your hoop is big enough, and your machine or embroidery software has the ability, you might want to look at enlarging the design WITHOUT increasing the number of stitches. There often are 2 options, one that makes the design bigger and adds stitches so the density is the same as the original, and one that uses the same number of stitches, but enlarges the design, thus making it less dense. You usually can increase the design by up to 20%. if you do this, you obviously need to stitch out a sample design.
When I got my first embroidery machine 20+ years ago, the instructor in the first class I took told us that the most important thing to learn is use appropriate fabric with your chosen design (and vice versa). In other words, a sturdy fabric can support a dense bullet proof design, while a lighter weight fabric is better served with a sheer design. Yes, you can add stabilizer, but the fabric isn't going to drape/lay nicely.
Whatever you decide, be sure and stitch out a sample, then launder it to make sure you are going to be happy.

The quilt I currently have on my bed has each block with an embroidered design. It didn't require any additional batting etc. I think each embroidered part is a four inch block with a triangle added on each side and then another triangle in a different color or print to make the squares. I then pieced them together to make it queen size once the borders were added. I probably used a wash away stabilizer for the embroidery. It is cozy warm and not stiff at all.

Most machined embroidery quilts I have seen feel stiff and formal. Like the hard images on shirts. There is way to do it so the images bend with the fabric and feel soft, I know there is because I've seen them. I don't machine embroider so I just go buy feel when examining the images.

I only do red work for quilts. Not stiff and looks great.