They do benefit. He was put on IR today, bringing the roster down to 23. The Canucks' upper limit will be reset temporarily to $81.33M instead of $81.5M while he is on LTIR. The team can exceed that temporary limit by Roussel's hit ($3M) on a prorated basis during that stint.
It seems to me that the page you quoted (which I’d read previously) supports my position that there is no benefit available.
Before getting to the workings of that page, I'll give a really simple way of looking at it. The Canucks’ total cap hit with Roussel and Gaudette both included, that is with 24 players, was $81.334 million. The salary cap it $81.5 million. The Canucks need no relief and they can’t use anything when they don’t need it. Long term injury relief isn't accruable for the future-what they don't use, they lose.
Now looking at things from the perspective of the page you referred to, you’ll see two different formulas for calculating the Accruable Cap Space Limit. The one for training camp situations is stated to be the difference between the team’s cap (before putting the injured player on LTIR) and the injured player's cap hit.
The Canucks’ total cap hit with Roussel and Gaudette both included, that is with 24 players, was $81.334 million, still below the salary cap. The Accruable Cap Space Limit using the training camp formula is $78.334 million, the difference between the team’s cap space before putting Roussel on injured reserve and his cap hit.
The Canucks’ ACSL is well below the league upper limit, by more than Roussel’s cap hit.
Their salary relief pool is Roussel’s salary of $3 million. Their performance bonus pool is 0 as Roussel had no performance bonuses (and wasn’t eligible for any, being neither on an e lc or a 35+ contract.)
Now the club is permitted to exceed the limit. The rough formula given on that page for the amount they can exceed the limit by is ACSL + Salary Relief Pool – League Upper Limit = $78.334 million + $ 3 million - $81.5 million which is a negative number, so there is no relief.
(That doesn't seem fair to me-it would seem that the Canucks should be able to spend up to the amount they were already spending plus the amount of the replacement(s) up to Roussel's cap hit, which would make an adjusted temporary cap hit of $83.417 million ($80.417 for 23 players including Roussel but not Gaudette plus up to $3 million for a replacement for Roussel. The regular season calculation for ACSL makes more sense to me. Either way, I don't see that the Canucks, with Gaudette as the replacement, are in a position to use the potential cap relief, though they logically should be able to use relief for performance bonuses Gaudette earns this season.)
That is consistent with a couple of other statements on the page you referred to.
1. “If the team operates below the ACSL, they begin to accrue cap space. A team can operate up to the ACSL without using their LTIR relief pools, once they operate above the ACSL, they begin to use their LTIR relief pools.”
2. “The ACSL will always be less than or (in the optimal scenario) equal to the league upper limit. The closer the ACSL is to the league upper limit, the greater the team will be able to exceed the upper limit.”
Note that the figure you’d given earlier for what the limit changed to was not the training camp formula. It works in mid-season when you start with 23 players on the roster but to do it that way you’d need to exclude Gaudette (as with him there were 24, which can't happen during the season,) which would leave the Canucks with over $1 million in available cap space, so that adding Gaudette’s salary back in still leaves you short of the salary cap.
All this is somewhat explained, in a roundabout way and not always very well, in numerous articles back in July when the the Leafs traded to get David Clarkson back to get their cap hit as high as possible before using long term injury relief.