MLB/NPB agree to deal

No, the Astros wouldn't automatically get Tanaka if they pay a $20m posting fee. The Japan Times says that MLB and NPB have agreed to a maximum bid for posted players, but the player would not automatically go to the team with the lowest winning percentage. See the following:

If multiple clubs willing to pay $20M, Japanese player can negotiate with all of them. Only the signing team will be required to pay $20M.
— Ken Rosenthal (@Ken_Rosenthal) December 5, 2013

For our purposes, that sucks. We're just assuming that Tanaka wouldn't pick the Astros and maybe that's the safest way to think about it, from an emotional standpoint. But don't rule out the sell job Luhnow & Co. could put on Tanaka. The Astros have money to spend and (presumably) payroll flexibility. That the $20m max bid is now in place, if the Astros were even in on Tanaka to begin with (and I can't think of a reason in which they would not), given that he was expected to command at least as much as Yu Darvish's $51m bid, they now have a whole lot more money to play with.