They will be champions, and they have punched above their weight in Europe.
But the danger signs are flashing that they could be holding on in the final few rounds of the title fight as they try to make it a league-and-cup double.
The mental and physical exhaustion was there for all to see at Dingwall on Saturday when, after a quick one-two should have left Ross County down and out, the Hoops allowed them to come back off the ropes to win 3-2.
It takes the total number of points conceded this season to what manager Neil Lennon considers to be an unacceptable 28, with his side having failed to go the distance in 11 of their 30 games.
The unhappy boss delivered a few blows to the solar plexus himself when he questioned whether some of his stars had been tapped up, and wanted to be here.
Lennon also called in his dues, reminding them that many had been plucked from obscurity to play for the club on Europe's biggest stage, and that they owed him big time for that opportunity.
The inconsistency of the performances has been a recurring and frustrating theme this see-saw season.
One week, this group of players are being hailed for their gutsy displays against some of the best teams in Europe.
The next, they are having everything but their parentage questioned for a lacklustre showing in a domestic game which should be well within their range.
Of course, the truth lies somewhere in between, and the major flaw in their makeup is the ability to focus fully when the stakes swing so viciously.
Playing for a place in the group stage or the last 16 of the Champions League is always going to produce more from within than playing Ross County on a bitterly cold day at the end of the A9 when, in real terms, the title is yours, whether you get three points on the day or not.
While that may be natural, it is, however, not acceptable, either to Lennon nor to the supporters who make huge sacrifices of time and money to follow them to such far-flung football outposts.
Given the achievements of the past seven months, the last thing anyone wants is for the season to be allowed to fizzle out.
They have already forfeited the chance to bag a rare Treble, and will next weekend face Aberdeen in the SPL when they could and should have been preparing to face Hearts in the League Cup final the following day.
With no Rangers to push them in the title race, they are doing enough and little more to ensure back-to-back championships – and that is not good enough, in the narrowing eyes of Lennon.
He is acutely aware how dangerous it is to take your foot off the gas, then expect to simply move up the gears again when it matters, which, to all intents and purposes, will next be when they face Dundee United in the Scottish Cup semi-final on April 14.
If they stumble that day, the SPL title will be all they have to show in tangible terms for the season.
While that was always the No.1 priority, it will seem scant reward for all they have put into the year.
Sure, there is a huge pile of money with which to fill the trophy, courtesy of their magnificent run in the Champions League, and the players have been richly rewarded for what they achieved in that competition.
But when they look back on their careers, they will want to do so with medals to show for their efforts.
In the same way, supporters and the manager want to be able to point to trophies won, celebrations enjoyed.
Lennon made the decision not to allow any of his players to speak to any media – including in-house – following Saturday's capitulation.
Perhaps he did not want them to relay the words which had been spoken in the dressing room when he left them in no doubt the consequences should they repeat such a display.
His own comments to the assembled media certainly underlined how personally affronted he had been by what he saw.
Having had any concerns about tiredness following their midweek trip to Turin and the long drive north on Friday eased by early goals from Charlie Mulgrew straight from a corner kick and Gary Hooper – back on target for the first time since the League Cup semi-final defeat to St Mirren on January 27 – what happened next was, to Lennon, as unpredictable as it was unacceptable.
As Ross County showed good football can be played on a bad surface, they got back into the match with a terrific volley from central defender, Grant Munro.
Just seconds before, Lennon had been spotted demanding his defenders didn't let their work become shoddy.
It did, then it became downright awful.
Sam Morrow took advantage of Mulgrew slipping and Dylan McGeouch sleeping to grab the equaliser before half-time.
And, in the dying seconds, not for the first time on the day, Kelvin Wilson was rooted to the spot while Fraser Forster appeared to have his mind elsewhere as a long punt into the box was allowed to bounce before sub Steffen Wohlfarth stooped to head over the keeper.
The good news for Celtic is that sojourns up the A9 should be finished for the season, although County were not projected to be a top-six club, so perhaps a third trip will be ordered.
Having drawn once – with a last-minute equaliser – and now lost – this time to a last-gasp winner – that is not a prospect which will lift the flagging spirits of Lennon's men.