The debate rages on about that. You'll find varying opinions depending on who you ask...
Years ago I might've told you who cares, toss it so you can easily open it up, do recaps, mods, etc. whenever you feel like it without having it in the way.
Nowadays I've learned a bit more on the importance of electronic devices being shielded as much as possible (as our FCC mandates). More so for old timer products like these.
Even for like a RGB mod, I'd tell you go the distance, use coaxial shielded wire instead of plain copper for each line and ground all 3, etc. So instead of simple copper, get the thinnest coaxial style with aluminum braid over it to send those video signals to your amp or YPbPr encoder and to the output port. Just like a RCA cable! It'd be harder but might be worth it.
So yeah, if it's not too much trouble I say leave it back in place and solder at least one contact to the (-) ground of the PCB. If it's not conducting (100% contact) to any (-) ground point, it provides no anti interference benefits.