Right now, the Oakland A's lineup would appear to look something like this:
2B Jemile Weeks
CF Coco Crisp
LF Seth Smith
RF Josh Reddick
Of course, I deliberately left the cleanup spot open. The A's have various candidates -- maybe they'll give Chris Carter a shot; Daric Barton is still hanging around, just one season removed from a .393 on-base percentage; they just signed Jonny Gomes.
Now, the reason why the A's would consider the move is clear: Even though he would have to first serve his 50-game suspension, there would be the hope that Ramirez hits well when he returns and the A's could flip him for a little something at the trade deadline. There is also the possibility, I suppose, that Ramirez would bring in a few extra fans to the ballpark, although if the A's want to do that they may as well sign Mark McGwire and Jose Canseco.
The reason not do it is pretty clear as well: The A's are going nowhere so why give at-bats to a 40-year-old Ramirez that should go to Allen or Carter or Michael Taylor or some other young player.
While I wouldn't be surprised if Ramirez has something left in the tank -- he did post a .409 OBP in 2010 -- I don't see the A's pulling the trigger on this. Even if Ramirez does hit, you're not going to get much more than a Grade C prospect for a DH-only guy. It may add a little fun to the A's season, but the A's need to be playing their young guys.