Blends can be achieved in embroidery. You just have to remember a few things.
1. The lighter color is going to be the bottom base color (which is also what encompasses the entire object) and the darker color is stitched "on top". On top is in quotes due to the fact that blending is actually achieved by interlocking the thread of the two colors, so they end up being one layer.
2. No underlay is put on the bigger base layer in order to achieve the goal of point 1. Which greatly impacts push/pull on the fabric. Especially when Picque fabric is used (polo). There are other fabrics that would have the same concern, but that type is the most common.
3. You have one stitch angle that is done on fill stitches, so if I gradient looks like it's going to need more then 1 angle to achieve the effect, then that type of blending isn't going to work.
Now when you start adding in ovals, text and borders that all intermingle with each other, one on top the other etc. Push/pull, registration become a concern. Some of those more difficult patterns are still possible, but if they choose something with a blend, oval and outline around the oval, the density, underlay, stitch order, angle are all going to be specific to one type of fabric. So if the pattern is setup for Picque, I wouldn't try to use that pattern on a hat or on cotton etc. You really shouldn't do that anyway, but some patterns can work on more fabrics and substrates then others. Depending on which one is chosen, that wouldn't be the case here. He might have to have 2 or 3 patterns.
You might want to have something for print and something for embroidery. I don't know their budget, but that might be something to consider.
Sorry Jill, I did it again. I just can't help myself at times.