Live & Learn...!
Is it possible...? Yes.
Is it smart to do...? Only if necessary
I was too impatient to wait for any replies... so I gave-it-a-go on my own.
Bottom-line: the two parts that need to separate: the clear dome on top... and the darker, grey-ish ring on the underside... are 'glued' or bonded together... NOT 'snapped' together.
Once you separate them, they are separated until you 'glue' them back together. It worked for me. I got to clean it all... then SuperGlued™ it back together with just a few little 'dabs' of the glue.
Mouse = clean
Is it worth doing...? That's up to you. I'm glad to see the 'gunk' out of there, so to me, it was WELL worth it. It 'looks' as good as new. (I was careful not to damage or scratch it during disassembly)
Attempt at your own risk.
Good day...!