I am going from the "will this work" part. If you don't know you can make a solid weld, running all the way down could harm a section that otherwise hold up, with one or more "good" welds and a few that wouldn't make it.
Also if you make it too solid you will just break the next part, thus the fuse part.
From the drawing I don't know the size or thickness of the part or where the forces go, so who knows how much flex is in the part(s). My first guess is enough to break off a few bolts.
Some times a "solid" weld can also weaken the part. The OP's drawings don't show intentions of welding the ends of the gusset but if there were length wise loads a weld would just make a shear point that was not there before. Plug welds or nothing at all would be better. Like the attached Komatsu forklift tilt support. They knew, from experience or testing than the mast lived better without welding everything.