That powerup storage was a single-player feature, not a multiplayer one. As such, it will not be implemented in multiplayer.
Seriously, imagine a Strogg player who saved up 4 quad/invulns. They could be invincible and quadded for two minutes straight. This is probably why this feature never left single-player in the first place.
Actually... it was a server-side flag in Quake2. Bit 4 (decimal value 16) of dmflags toggled this feature.
The
default settings was to enable 'instant powerups' but you could disable that. And quite a few servers I know of did disable it, 16388 was a common DMFlags setting that I ran into a lot, which was very simple. Quad Drop, so if you manage to kill the bugger you can loot his shiney blue glow from his corpse, and Weapons Stay, much like Q3A. :-)
As for holding 4 quad damages... what was taken care of quite easilly. You could never hold more than one in deathmatch, as I recall.
So, yes, you could 'save' the powerup if the server allowed it, but you couldn't stockpile them.
(Edit: More specifically, you could never 'carry' more than one Quad Damage, for instance. You could 'carry' one while one was in effect, effectively letting you 'chain' together two Quad Damages, but that was the limit.)