Not really. Tax-exempt status in the US prohibits donated money being earmarked. It also can’t be used to funnel money to arbitrary affiliates - they’d need to satisfy the permissible tax-free mission of the org. Plus those affiliates are going to end up paying the tax themselves. Without a clear picture of where the money is intended to go, it’s unlikely such an org could obtain tax-exempt status in the first place.
Note: tax-exempt status has become harder to obtain in recent years for open source projects.