But the appeal almost certainly won't be heard before the third Test between Australia and South Africa starts in Adelaide on Thursday.
It's understood the tourists were furious with Pycroft's guilty verdict, having initially dismissed the allegation as a joke.
The other side of the argument, as put forward by some pundits after the verdict, is du Plessis should not be taking the field on Thursday.
Du Plessis was found guilty of ball tampering in 2013, when he breached the ICC's code of conduct by rubbing the ball on the zipper of a trouser pocket during a Test against Pakistan.
But as per the new ICC code of conduct adopted in September, the indiscretion in Hobart was treated as a first offence.
In addition to the fine of approximately $2500, three demerit points were added to du Plessis's disciplinary record.
The batsman was all smiles at Adelaide airport on Monday, when the Proteas' head of security physically clashed with a journalist, but his demeanour changed significantly the following day.
Du Plessis stormed across the field after his hearing, while Australia conducted a fielding session nearby.
Coach Russell Domingo, speaking prior to the hearing, stopped short of saying the Proteas were being unfairly targeted.But Domingo made his thought on the matter clear, expressing the same indignant sentiment that was put forward by veteran Hashim Amla last week.
"There are other teams that have maybe done similar things and we have maybe looked at one or two instances that they have done those things - and those things haven't been highlighted," Domingo told reporters on Tuesday.
"It has definitely been brought to the attention of the world ... it seemed pretty insignificant at the start of it all, so I think quite a lot has been made of it.
"We are a unified team. We stand by our captain.
"It's never pleasant when everybody has got an opinion on you and people have judged you before the rulings have been made or decisions have been made."
Domingo suggested the du Plessis case could be a watershed moment for cricket's rules regarding ball tampering - insisting mints or lollies to assist shining the ball is considered common practice.
"You see it daily with, I suppose, those types of incidents taking place in the field," he said.
"So they might need to look at it should they feel it's not within the spirit of the game."