If you want to keep the same number of squares that make up the block, the large white is equal to a 5x5 unit. Now, you can make the block so that the dresden overlaps the seams and takes up more of the "white" area, or that it stays within the large white block. In that case, those five across would need to measure at least 17", and 17/5 =3.4". So you could round up to 3.5" and then cut each square at 4" and sew together. The large white will be 3.5" x 5, or 17.5" finished cut 18".
This is going to make each "block" 24.5" square, so you might only have "room" for four blocks by five blocks, and that isn't going to make for much of a chain pattern. Maybe save those dresdens for another quilt, and make smaller ones to use with the Irish Chain pattern.
However if you have one Dresden and you want to use this idea for a medallion style quilt, I think that would look really neat.