No, that wouldn't help us at all.
When a player goes on LTIR, their cap hit doesn't actually fall off from the team, the team just gets a cushion to go over the cap by exactly the amount they need to.
So math exercise:
Next year, cap ceiling of 82.5M. Let's say the Wild come in at 82.2M without Weber. That means we'd have 300k in cap space. If they then add Weber into the mix, putting him directly onto LTIR for the season, then yes, the Wild's cap ceiling would be 82.2M+7.86M. The problem, is people are under the misunderstanding that Weber's cap hit falls off, but it doesn't, it still counts against us. So all of that additional cap space above the 82.5M ceiling is already earmarked for Weber, and the entirety of the 82.2M and below cap we had prior to Weber is obviously earmarked for the players who made up that 82.2M prior to adding Weber.
Some teams (like Arizona maybe) will look to acquire LTIR contracts because, since their cap hits still count against the team, it helps them reach the cap floor. But a team like the Wild acquiring Weber, we don't gain anything from that.
LTIR only helps a team if it's one of their own players going on it. So if Dumba were to go on LTIR right now for the rest of the season, we would effectively be able to add another 6M in players to the roster for the rest of this season. But if Dumba was going to come back before the end, we would need to clear 6M to get back down to the 81.5M cap ceiling.
It's a little confusing, but the tldr is that acquiring Weber provides us with no benefit.