"Needed" is the key word. No, it's not needed, and it's always subjective. There's no way to replicate a full system overhaul with just a speaker swap. With an 800a, at least it's easier for you.
However, if you just want to try a speaker upgrade first, I'd try some 6x9 components from JBL/Infinity. Can be had for $150 or so, and are 3ohm speakers designed to play louder off factory amps alone. If that's not enough, then upgrade further. I would not bother with the rears unless you add an amp.
I did JBL speakers only in my 2018 802a and it made a noticeable improvement, especially from the kickpanel mid-bass drivers. The stock units there are literal paper/tiny magnet crap. Good luck, whatever you choose.