I am making a quilt for my GD and I have embroidered in some of the squares. So I say go for it!
Dawn

One way to do your squares is to cut the square to size then just place it inside the hoop with stabelizer then sew the design. As for using floral material, YES you can do nice red work, here's my quilt on floral material.

My method is to first embroider your design, then cut it to the size you want (that way it will always fit in your hoop) then sew your squares or blocks together in your desired layout, the lay out the backing right side down, put your batting on top, then your quilt top right side up and pin with safety pins all over keeping it smooth. If you have a long arm or access to a long arm you just load it on and have a blast, binding is last of course. Have fun and don't forget to put a label on the back so 100 years from now people will know you made it!

I would embroider first, then put together. And it's your choice for the fabric. What ever you like. AND sometimes really wild things look great. I did a couple of shows with a lady who made jumpers. She put some of the most horrible colors and prints together. I would never have even put them on the same table let alone the same dress! BUT I really liked every one of her dresses. It worked on what she did. So let your mind run wild!

I would embroider first,also. Cut the squares to be embroidered oversize so you can square them up to exact size before putting in your quilt. As to doing embroidery on floral prints,Just do a sample to see if you like it or would the embroidery show off better on a plain fabric. It is yor choice!

If you are speaking of the quilt squares that are open and not a dense design,like below, then you can use those designs as the quilting in those squares. If you have the quilters hoop (150x150), you just hoop the square using the think fabric inside hoop with no stablizer and use the design as the quilting. If you do not have the quilters hoop, your backing, batting and quilt top will be too think to hoop with a regular hoop. I would try doing a sample first but use a light tear away and use the "fix" on my machine to hold the quilt on the hoop. Maybe even a light spray adhesive before laying on the quilt. If it is a dense design, I'd do as the others suggested, embroider first. Can't wait to see what you've done.

Here is a link to show how to quilt as you go.

Another link:

I do mine with the squares cut and the batting cut to size to fit the hoop of my machine ME then make the cuts to fit the pattern of my quilt then piece together making a top with the batting I use the cotton thin batting and use it as part of my stabilizer then put together like a quilt and either tie the quilt together to make the back be attached or do quilting around the ME design in the blank areas hope this help I have one that I have done in the project area Tea party quilt sorry it been their for a while and I don't know how to add the urls links