Definitely, it's super weak but at the same time constructive. The issue is that it essentially ends up becoming a search algorithm where contradiction is backt

Definitely, it's super weak but at the same time constructive. The issue is that it essentially ends up becoming a search algorithm where contradiction is backtracking. If the search algorithm doesn't stumble upon the solution (at least in principle) in finite time then it's a bit tough to consider it constructive.