Alcock underwent surgery for appendicitis and is extremely unlikely to be right to take on the Crusaders.
The Waratahs injury woes were further compounded with fullback Bernard Foley already being ruled out of Sunday's match.
Scans have revealed Foley aggravated a previous shoulder injury during a tackle gone wrong against the Melbourne Rebels on Saturday and he's expected to miss up to three weeks.
The Waratahs, who sit second behind the Brumbies in the Australian conference, face a mini-personnel crisis for the match.
Foley's loss has been compounded by a foot ligament injury to interchange forward Paddy Ryan.
On top of that, centre Rob Horne has been rubbed out for two matches by the judiciary for his dangerous tackle on Kurtley Beale.
Already on the long-term casualty list for the Waratahs are Dan Vickerman (shoulder/leg), Drew Mitchell (ankle), Lachie Turner (hamstring), Damien Fitzpatrick (knee) and Pat McCutcheon (ankle).
The Waratahs are taking some momentum into their meeting with the Crusaders after recording back-to-back wins for the first time this year against the Rebels, however having their depth tested will give an entirely different complexion to Sunday's game.
The Waratahs showed signs of improvement in their derby victories over the Force and Rebels, but the Crusaders, runners-up last year, are on a different level to the Australian conference battlers.
Foley will be assessed on a weekly basis but isn't tipped to return until Round 12 at the earliest.
Waratahs coach Michael Foley said he would consider No 10 Berrick Barnes as his new fullback, but Adam Ashley-Cooper shapes as the other option.
Prop Ryan sustained a Lisfranc (mid-foot ligament) injury to his right foot.
His recovery is anticipated to take at least six weeks, meaning his return is unlikely until after the international window.