Wow, I have never seen one with that big of lines.. Im relating it to hydronic piping, that I deal with at work.
I would never run a 1" pipe and then up size to a 2", then reduce to a 1" again.. just poor practice, would it work yes. Although, its not optimal, you have good velocity and pressure and then open up to a larger size and loose it, however its reducing again and being forced back to that smaller size. It will work, but I dont know if over time it will cause any issues or will work just fine, it could be hard on the pump as well.. Myself I would look for a 3/8" inlet outlet, but thats just me.. Not to mention is it going to look odd making that transition from 3/8" to 5/8" where ever your going to mount it?