Now Alpha does not own enough to block this so it would greatly depend on if 15-20 percent of other share holders feel the same. If Alpha holds its stance in wanting a higher offer I am pretty sure it will be close vote either way. I doubt TPG needs to offer 6.50 to get this through but adding another 30 cents plus to the price could definately help making it over the line in the share holder vote.
Of course we do have the risk of TPG walking away but personally I think it is likely that they have some flexibility on their original offer. If TPG was really serious that this offer would be their max price they could offer then they would have been best to say that from day one. But then they risked another company bidding even just a few cents higher. Also I still think a decent percentage of shareholders that have held this stock for years, a very large percentage of them will likely vote this down.