"It's been exaggerated all my career," he says of his reputation as Wigan's Good Time Charlie. "People have taken it the wrong way. I like going out with the lads for a drink and a laugh, but there's a time and a place for it. You've got be responsible. I'm always here when I should be and I'm one of the best trainers at the club."
His coach, John Monie, does not disagree with any of that - although, like all Connolly's coaches, he has kept a dubious eye on his liquid intake. "He's an enigma," he said. "He has his injury problems and you see him struggling on his dodgy knee at training, but he lives with it and keeps up a remarkable level of consistency in games. He's so durable, but he's also got so much pace. And he's the only fellow who's beaten Malcolm Reilly at arm-wrestling."
That makes Connolly an enigma bordering on a freak. His remarkable combination of speed and strength is achieved despite burning the candle at both ends and sometimes in the middle. Kris Radlinski took his life in his hands by going on an end of season trip to Tenerife with him last year. "He's slowing down a bit now he's getting older," he said.
But, at 27, Connolly remains the exception who proves that it is still possible to be an outstanding player without adopting monastic vows. "I've no doubt that he's the stand-out centre in the English game," Monie said. "He's a real talent, but what he's really known for are his defensive qualities. Even when you see him up against someone like Paul Newlove, nothing gets past him at all."
As will probably be evident in tonight's battle with Leeds for a place in Super League's Grand Final. His centre partner today, Danny Moore, would vouch for that. When he makes the first tackle low and Connolly comes in second to wrap up man and ball simultaneously, Moore just feels the air go out of the victim.
The damage is done by a player who looks physically innocuous. The features of a choirboy - albeit rather a raffish one - and the constitution of an ox; that's Gary Connolly.
A fascinating player is now at a fascinating stage of his career. One of the British players to sign for the Australian Rugby League during the upheavals of 1995, he is due to join a club - it could be any club - there in June. Negotiations to keep him at Wigan instead have gone on longer than a Tenerife pub-crawl. "I've played in Australia before and liked it out there. But if Wigan's offer was the same, I'd probably stay," he said.
One effect of his ARL contract has been that Connolly has not played for Great Britain since 1994. "I'd been there and done that, so that eased it for me. I was really disappointed, but it gave me the chance to have a rest and also the chance to play rugby union, which was something I wanted to do." Connolly's spell at Harlequins was the most successful of that code-crossing winter, with his tackling making a particular impact. "All the lads there were great with me; better than I thought they would be," he said. The only disruption to his enjoyment came when he was misrepresented as saying that Will Carling, would not have made it in rugby league. "I never said that," he insisted. "He would have taken a lot of stick, but he would have come through and made it."
If his rugby league form suffered last season from year-round activity, he has been back to his best for Wigan this time. "I've had some good games and some bad games," he said, cautiously. "As long as I feel I've gone out and tried my hardest I'm reasonably happy."
Two of the games with which he is not entirely happy were, logically enough, the two Super League defeats by Leeds. "When you've had defeats like those, you go back and think that you could have done this, could have done that. We could have won both games."
Connolly rates Leeds' first-choice centres, Richie Blackmore and Brad Godden, as the best pair he has faced this season. "A lot of people didn't know who Godden was when he arrived this season. He's a typically good Australian defender, but he's also very good when he gets into the open."
But Godden won't be Connolly's toughest opponent. That title is reserved for Reilly, the competitive former Great Britain coach, who met his match with the deceptively callow 20-year-old on the 1992 Australasian tour. Reilly, who describes Connolly in his autobiography as "a bit of a wild boy who loves nothing better than a night out at a club and a late party", took delight in being able to arm-wrestle all his players into submission. Not Connolly. "He didn't take it too well," the player recalled. "He called me a cheat and everything. He's been trying to get the better of me ever since."
As plenty of others have found, you have to get up early in the morning - or stay out very late at night - to do that.