Wenger hesitated before pointing out that there could be no definitive answer
That suspicion can only be reinforced by thinking back to the corresponding fixture last season when Arsenal actually played much worse but still beat Sunderland 2-1, with Van Persie conjuring exquisite finishes in the first and 82nd minutes of the match.
Wenger’s hopes now rest with Lukas Podolski and Olivier Giroud but, as he himself acknowledged, their combined 39 goals in Germany and France last season do not necessarily replace Van Persie’s Premier League tally of 30.
For one thing, Wenger does not currently see them as a pair and, when Giroud was introduced on Saturday, it was as a straight swap for Podolski in Van Persie’s old role as the main central striker.
The system, though, never quite clicked as Podolski, in particular, struggled to link Arsenal’s usually fluent midfield and attack.
“He has some work to do to change his game, make runs in behind and to protect the ball and move around the box,” acknowledged Wenger. “But I’m positive he will get there because he is a fantastic finisher. I have to study it. At the moment we cannot say it worked.”
Giroud was culpable for wasting Arsenal’s best chance on Saturday but, in pointing out that Van Persie had been at Arsenal seven years before producing a season like his last, he made a valid point.
“In Montpellier, I did not score for my first game so I’m not worried,” said Giroud. “People are clever enough to know that Robin took a lot of space here. His last season was wonderful but, before that, he took time to settle. So I’m just asking people to be a little patient with me.
“I know Arsenal is a great club and needs a striker ready and efficient quickly. I’m not here to make people forget Robin. He has made beautiful things here – I just want to bring something new.”
With Alex Song also departing, Arsenal do face an inevitable period of adjustment but, with some fans booing the final whistle, it is also clear that patience is already in short supply.
One sizeable consolation was the performance of Santi Cazorla. He was behind all of Arsenal’s best moments, forcing an acrobatic save from Simon Mignolet and producing a wonderful reverse pass for Giroud’s chance.
“He looks certainly for me one of the buys of the season,” said Wenger. “He has everything you want in the game. He can play short, play long, right, left, can play the final ball and works hard as well. He is a fighter. It’s very positive.”
Martin O’Neill, the Sunderland manager, is still searching for some bargains of his own before the end of the transfer window, particularly in attack.
Steven Fletcher, the Wolves striker, is one option although Sunderland must also resist any interest in Kieran Richardson, who has indicated that he may want to leave for family reasons.
“I’ve got a number of situations here,” said O’Neill. “I’m trying to get players in, not losing anyone or I’d be down to about four players.”
O’Neill was more forthcoming, however, on the challenge Arsenal now face without Van Persie. And his assessment will offer little comfort to Arsenal fans.
“It’s a major, major loss,” said O’Neill. “Real Madrid would suffer if they lost Ronaldo; Barcelona would suffer if they lost Messi – Van Persie was every bit as important to Arsenal.
“You think you’ve got everything, you’re playing for Arsenal and then you decide that is it. What more can a manager do? You’ve got an unhappy player here for a year and he plays under duress or do you decide to take the money?
“In an ideal world I’m sure he would have preferred him to go abroad: out of sight and out of mind. But he decides to go to Manchester United and that’s as bad as it gets.”