I don’t think this will work well, especially if the groove go all
the way around the ring.
1- you will most likely have pitting.
2- solder will wear away more quickly, leaving recessed areas in the
grooves, especially using yellow solder in a white gold band.
3- the oxidation that forms in areas ahead of your solder will give
you fits and lots of extra work.
Could you fill the design areas with wire instead? This could be
soldered in place, or, if it goes all the way around (forms a ring in
its own right), perhaps a friction fit will be adequate. Many
commercial 2 tone bands have been made with only a friction fit,
usually with flanges formed at the edge to hold the center element.
If the design is too irregular to use wire, I would fabricate those
elements from sheet and inlay those pieces with solder. Jim