This is incorrect.
This belief stems from a previous misinterpretation of CBA language that says that Asante CURRENTLY counts against the cap in an amount equal to the size of the tender.
Once Asante signs, his cap hit will equal the total number of dollars that he is scheduled to be paid in 2007. Every game he misses before signing the contract will reduce his cap hit. This money will then be available for other uses (such as pushing it into 2008 via faux LTBE incentives).
[I think that the CBA language is ambiguous as to WHEN the extra money becomes available. I would expect Asante's cap hit to be reduced each time he misses a game, but the language also supports an interpretation that no money becomes available until Asante signs his contract (or the Patriot's withdraw the tender). Either way this is completely irrelevant since Asante will be reporting before the first game.]