But in the bigger picture, is it a really a result in their favour from a week of reverses?
The referee who cautioned the Nigerian twice inside eight minutes in the dying stages of Saturday's 6-1 drubbing by Spurs in Helsinki has used his discretion and not included the dismissal in his official report, which means no further action from the SFA.
Given that Charlie Mulgrew had to sit out a league game at the start of last season after the ref did report him for his red card in a friendly against Ajax, that's at least one bit of good news for Ronny Deila.
Or is it? Ambrose is banned for Wednesday's crunch Champions League qualifier against Legia Warsaw at Murryafield after being shown a straight red in Poland just before the interval in the first leg.
Perhaps an extended period on the sidelines is precisely what is required at this point for the player who has claimed that he never needs a break "Because I am Efe" .
The 25-year-old defender may not think he needs it but the evidence is mounting that he most definitely does.
His body might be in shape at present, despite Ambrose having played without any down time for more than two years due to his commitments with Nigeria at the African Cup of Nations, the Confederations Cup in Brazil and, most recently, the World Cup finals.
But his mind appears to be toiling, manifested in the poor decision-making of which he has been guilty.
The aberration which led to his dismissal in Helsinki was final proof that Ambrose is thinking through a fog.
His presence was supposed to help the extremely youthful team pitched in against a Spurs side which, at one point, brought on an array of talent valued at over £100million.
The first booking was for the rash foul which led to Christian Erikssen scoring Spurs fifth from a free-kick. Minutes later, he was also adjudged to have brought down Danny Rose for the penalty which allowed Emmanuel Adebayor to step up to the spot and put the ball past Craig Gordon for the sixth time.
But having got his name in the book he then committed an unnecessary foul on Adebayor a few yards inside his own half, giving the ref the opportunity to show him a second card. It was irresponsible from such an experienced player.
Quite how Deila viewed his actions as he watched on from back in Glasgow - where he'd remained with the first-team players who will be asked to save their Champions League season this week - Ambrose will by now have discovered.
The new boss might still have been looking through the cracks of his fingers as his side suffered in a friendly arranged before he took charge and which, coming between the two Legia ties, they could certainly have done without.
Hence the decision to send the boys, instead of the Bhoys, to Finland, with only Ambrose, captain-for-the-day Teemu Pukki, Liam Henderson and Dylan McGeouch boasting anything more than the briefest association with the first team.
GORDON should have added some much-needed experience and calming influence to those in front of him.
But even the 31-year-old keeper got exasperated at his side's inability to stop Spurs cutting through them at will.
The former Scotland star got particularly animated with Ambrose when the defender allowed Lewis Holtby to step off him and pick up the ball to slam home goal number three a minute before the break.
Harry Kane and Roberto Soldado had scored the first two inside 12 minutes.
Teenage midfielder Jamie Lindsay was credited with Celtic's goal a minute before Tottenham regained their two-goal lead.
With full internationals Adebayor, Erikssen, Erik Lamela and Aaron Lennon among those to come on for the English side after the break, there was never going to be any chance of the Hoops kids mounting a fightback.
And a deflected shot from Lamela, a fantastic free-kick from Erikssen and Adebayor's penalty appeared to have completed Celtic's miserable day.
That was until Ambrose - who conceded the free-kick and penalty that led to the Premier League side's final two goals -capped it with his dismissal.
Yes, it was only a friendly. But it was the timing of the defeat, and the margin of it, that has hurt a club already battered and bruised by recent events.
Even the Spurs boss Mauricio Pochettino was unhappy as he had wanted a stiffer test for his side building up to their new league season, which kicks off in a fortnight.
His disappointment is of little concern to Deila, who has more important people to appease - namely the Celtic support and his employers. Whatever he and his squad worked on at their Lennoxtown training base over the weekend will become clear the moment the whistle goes at Murrayfield on Wednesday and the recovery mission against Legia Warsaw begins.
AMONG those who did not travel to Helsinki was Jo Inge Berget, who made his debut in Warsaw just 48 hours after signing for Celtic on loan.
The midfielder might have been looking to improve the match fitness and sharpness that was clearly lacking against the Polish champions.
The fact he stayed in Scotland is an indication he remains part of Deila's plans to turn this tie around, and that the manager is once again prepared to gamble, using his faith in his fellow Norwegian as part of his stake.
Reshaping the Celts' back line will have been major part of the work done behind closed doors at Lennoxtown. Finding a dependable partner for Virgil van Dijk is crucial to their hopes.
Moving Charlie Mulgrew from midfield to partner the big Dutchman for the second half in Warsaw last week did not bring the stability required.
Of course, with the need to score at least three goals paramount, honing Celtic's attacking edge will also have been a priority over the last few days.
But without a firmly closed back door, the Hoops could find scoring goals at Murrayfield is not enough to prevent their Champions League journey coming to an abrupt halt near a tram stop in Edinburgh.