If I'm reading the CBA correctly, there seems to be some confusion about the impact of players cut ahead of the date but designated as June 1 cuts.
If a player is designated as a June 1 cut, the contract (and salary cap impact) still stays in place through June 1, even though the player is able to immediately sign with another team. Therefore, any cap room generated by the move isn't available until June 2, or well after the prime free agent signing period. Cutting a player outright (no June 1 designation) puts all the dead money in the current salary cap year, but it also recognizes any money saved against the cap immediately, making it available to sign free agents as soon as the player is cut.
If anyone out there thinks I'm reading this wrong, here's the language from the CBA (Article 13, Section 6 (ii)(1), (Bolding added for emphasis). I'd welcome any guidance correcting my understanding.
Additionally, here's a snippet of an article from "Under the Cap.com" from last off-season that addresses this topic, and seems to confirm my interpretation. The example used is for Steve Breaston, who was released by the Chiefs in Feb. of 2013 and designated a June 1 cut (once again, bolding added for emphasis).
So in essence, if the Texans cut Schaub today and make it an outright cut, they've generated $3.625 Million (Current cap hit of $14.125M less dead money of $10.5 M), whereas if they cut him and designate him a June 1 cut, they generate no cap space until June 2, at which time they would get $10,625M in space, but also see the difference of $7M count against their 2015 cap.
So the final question is - if there's no cap benefit to a June 1 designation, why do it? Well, it gives the player a head start on signing with another team, but I can't really think of an example of the team benefitting, so if anybody else can, pass it on.