The only reason Hasbert would become President through would be if Bush chose him as his successor. The chain of succession is in place for sudden loss of the head of state, such as from a decapitation strike. When it becomes a pre-mediated affair, the President (working with his current VP) has more than enough time to pick whoever he wants to become President by selecting him (or her) to be step into the position of VP.
Mmm, not quite. Much like a judicial nominee, any VP selection made by a sitting president needs to be approved by a majority of both the House and the Senate. If the post-Katrina situation had devolved so badly that there was legitimate pressure on Bush to resign, even the then-Republican Senate would be unlikely to give him
carte blanche, and his hand would hardly be free. Bush could appoint a hand-picked successor as
acting VP, but until confirmed by the Senate, that individual would not be included in the line of succession.
Bush might try to pick a noncontroversial figure for the role, in hopes of getting Congress to act quickly on confirmation. But I can't think of any really acceptable candidates who would've been able to sail through Democratic opposition who wasn't
already in the line of succession, at which point it becomes considerably easier for Bush to arrange things informally with Cheney, Hastert, Stevens, et al. for each of them to step aside and make way for a chosen successor. Under these circumstances, I think the most logical choice would have been SecState Rice (fourth in line). But it's hard to say what Bush and Cheney's strategy would have been, under the circumstances, or whether or not Denny Hastert or Ted Stevens would've been willing to cooperate with a president so unpopular he was facing resignation.
Also, to correct a comment made upthread, Robert Byrd was not President Pro-Tempore of the Senate in 2005. The Democrats were in the minority in both houses of Congress, so the position was then held by Ted Stevens (R-AK).