Cotter became a legend at the French club when he ended their infamous trophy drought by delivering the league title in 2010, but in the three weeks before his departure he oversaw a humiliating loss to Saracens in the Heineken Cup and the surrendering of a 77-game home winning streak in their defeat by Castres in the Top 14 Championship.
Even if Cotter can announce himself as a Test coach by steering Scotland to wins over the United States and Canada during the North American leg of their globe-trotting summer tour, those losses to Saracens and Castres will eat at him for a long time. But in selecting his first international team, to face the US Eagles at Houston's BBVA Compass Stadium, he has already discovered the world of difference which separates stewardship of club and country sides.
The Scotland squad he has brought here has been compromised considerably by the need to hold players back for the second section of the tour, which takes in Argentina and South Africa. Cotter is also missing players who, although fit to play, have been held back in order to undergo elective medical procedures. Cotter was ruler of all at Clermont; from now on he is just part of the machine.
Would he have picked tomorrow's team diferently without those restrictions? Almost certainly, but perhaps not radically. The home-based debutants, Finn Russell and Gordon Reid, have played their way into the side and were probably the form men in their positions in Scotland towards the end of the season. That might not apply to Blair Cowan, the other debutant in the starting line-up, but a Player of the Season award at London Irish is not to be sniffed at - and neither are his stamina and versatility in what is likely to be a physically draining contest.
Cotter would almost certainly have chosen a different centre partnership, but with Alex Dunbar and Matt Scott both injured, and with the Eagles looking strong in that area, Sean Lamont and Duncan Taylor offer the grunt and defensive presence which could be the most important qualities in that area of the pitch.
It is also a hugely welcome development that the back three combination of Stuart Hogg, Tim Visser and Sean Maitland that won such high praise in the 2013 RBS 6 Nations Championship has been reunited for the first time since that tournament. Two of that trio were Lions in Australia last year, and the third probably should have been. The USA will ask questions of Scotland tomorrow, but the Scots can unquestionably pose a few of their own.
Yet nobody who has witnessed the emergence of Reid, and witnessed his evolution from being a decent prop at Ayr into a top-notch professional, would disagree with the proposition that the Glasgow Warrior's presence in the starting line-up is the most heartwarming element of Cotter's first selection.
Reid missed out on the development programmes, the fast tracks and the hot-housing that the SRU had in place a few years ago, and made his living as a barman, a pub bouncer and a French polisher before he threw in his lot with the Warriors.
Lesser players would have given up long ago and it is easy to suspect that Cotter, who once described himself as "just a kiwi sheep farmer", admires that self-belief and perseverance as much as anything the fellow can do in the scrum.
"It puts you in good stead," said Reid of his former life yesterday. "It makes you think about things instead of starting rugby at a young age and not having any kind of career. It gave me the attitude and drive to push on. I don't want to go back to that. I want to push on.
"I found out I had been picked for Scotland on Wednesday, when the team was announced. I was obviously over the moon to be starting. It's unbelievable. The jobs I did in the past got me to where I am now and you should never forget where you come from."
Reid was hailed as a hero by Glasgow fans in the semi-final of the RaboDirect PRO12, when he replaced Ryan Grant early in the game and went on to deliver a superb performance, capping it with the decisive try. Reid was subsequently picked ahead of Grant for last weekend's final in Dublin.
It was a testament to the pace of his improvement over recent months to be chosen before a recent Lions tourist, but, having packed in a transatlantic flight since then, you have to wonder if his energy levels are quite where they should be.
Well, wonder no more. "It's quite hot," said Reid, revealing a gift for understatement to go with all his other talents. "We had a blow-out on Tuesday that was really good. It nearly killed me, but that was what we needed. We trained today [Thursday] as well and that has pushed us forward and we feel much better.
"I feel great now. The travel and the time difference was a bit hard but we are professional rugby players and this is what we do for a living. We have to overcome these situations. But all the boys feel great and are buzzing for this game."