Lock Nathan Hines (bruised ankle and knee), flanker Allister Hogg (dead leg), winger Sean Lamont (ankle) and full-back Rory Lamont (bruised shoulder and hip) all picked up knocks in the weekend win and missed training both on Tuesday and Wednesday.
Centre Andrew Henderson's dead leg had ruled him out of the Portugal match, while scrum-half Rory Lawson "tweaked his back" during a weights session earlier this week.
Hadden would therefore have been delighted to see only one of the injured clan - Sean Lamont - not feature in training on Thursday.
And the Northampton star is expected to be back on the paddock on Friday for the Scots' penultimate practice session before they return to Edinburgh on Sunday, ahead of Tuesday's Pool C match against Romania.
The older Lamont brother was not the only squad member to be absent from training at L'Etrat, a village to the north of St Etienne, on Thursday.
Gavin Kerr missed out as he was sitting a surveying exam in Lyon, but the prop will be back in training on Friday, a Scotland spokesman confirmed.
The squad were interested observers last night as the Romanians took Italy all the way in their pool match in Marseille.
The Azzurri ground out a 24-18 victory to earn their first points of the campaign but they failed to claim a bonus point.
And Daniel Santamans' men did enough to suggest they will be no pushovers next week, unlike the last time Romania came to Murrayfield - in November last year - when they were thrashed 48-6 by the Scots.
"I wasn't really surprised (with last night's scoreline) because Romania are a physical team and they can do some damage," Rory Lamont said.
"The last time we played them, they were missing a lot of their players who play in the French league so we know it will be a lot tougher when we play them next week.
"Italy have some great forwards, and for them to struggle like they did last night shows that Romania are a strong team. We obviously know about their pack and their scrum but they have other good players."