Absolutely. What are you using for paint? Most of the frame and chassis paints (chassis saver, POR, Truck and Implement, etc) only require you to remove loose material. As long as you cut the oxygen off from the rust, it won't spread. If you really wanna get crazy, Wire wheel it, then hit it with a rust converter, which converts the active iron oxide to an inert compound (not a chemist, so I don't know the exact science), then prime and paint. This is the process I follow, if the part is too big or complicated for my media blast cabinet. It has worked for me so far on a few lawn and garden tractors from the 60's...
Honestly, looking at the photos, I don't know that I would even bother with the 44. Clean it up, and hit it with semi-gloss Rustoleum Professional Spray bomb if you want it to look all Brand-New. The HP30 looks dirty, but doesn't look rusty. Take it to the car wash, spray it down with the high pressure, the use the engine degreaser, rinse, then use the soap and a rag, High pressure rinse again. Judge it then...If there is loose material, knock it down with the wire wheel, clean it up again (I use acetone or Rubbing alcohol) and prime and paint.