Cooper was unable to join his team-mates for Friday's captain's run at St Josephs College after coming down with a stomach bug overnight.
Winger James O'Connor and full-back Kurtley Beale both ran at fly-half during the soggy 45-minute training session while the Reds superstar was confined to his hotel room.
Veteran Matt Giteau, who was controversially omitted from the 22 on Tuesday, did not train with the squad and has not been placed on standby for Cooper.
While the playmaker's absence from the session was far from ideal, Elsom played down the disruption and declared the number 10 a definite starter.
"I think he'll be all right," Elsom said.
"I think it was probably a good move not to train but I think he'll be fine tomorrow.
"It was all right (not having him at training), you've got to be able to deal with that and if he's not feeling that well then it's best he just gets better and feels better tomorrow."
Elsom also has no concerns over the state of the ANZ Stadium surface and is confident his side can adapt to the wet conditions after around 200 millimetres of rain fell on Sydney over the past three days.
The venue for Saturday's Test will also host the Bulldogs-Eels NRL clash on Friday night.
"I'm not too concerned about it because if it's wet it's going to be like that (cut up) anyway," he said of the pitch.
"So the game might be a little bit slower but I think if it was really badly cut up and really dry that would be more of a concern.
"We've got a game plan that we think can adapt to both (wet and dry conditions).
"Obviously if it was like it is now (heavy rain) it's not going to be as free flowing, but that's not necessarily a problem."
Elsom emphasised the need to stay disciplined in the wet given Morne Steyn is in the Springboks line-up.
"When you get into a game that's potentially a little bogged down points become more valuable, and with a bloke like him on the pitch your discipline's got to be right up there," Elsom said.
"We've spoken about that as a group but I guess the proof will be in the performance tomorrow."
Asked what he is expecting from Peter de Villiers' under-strength side, Elsom replied: "We've got an idea how we think they might play...but they do a pretty good job at what they do nearly all the time so we've seen a fair bit of that in the past.
"Yeah they're physical and it's a physical game but I guess every team is physical.
"I think it's who is the most dominant on the night that counts, and if they're more physical than us or they win that battle, then they'll go a long way towards winning the match and vice versa."
The Springboks are expected to target Australia's Pat McCabe, who has been selected at centre despite playing full-back for the Brumbies.
His opposite number Wynand Olivier told the Herald: "I didn't expect to see [McCabe] there because he is a full-back. I haven't actually seen him at centre except for last weekend. But he did quite well.
"I'm going to look forward to playing against him, I think it's going to be a good challenge for me.
"I'm going to try to see if I can squeeze past him once or twice.
"It is international rugby, they wouldn't put him in that position if he couldn't handle it. He is a good player, I am looking forward to playing against him."
He added: "Against the Wallabies we are always prepared for a physical confrontation, but even if it rains we will go with what we have trained in the last few weeks."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.