Souza is not a huge loss. I took a quick look at him when I reviewed the Diamond Jaxx earlier this week, and he is what he is. He has decent control, but he's more of a fly ball pitcher and does not work deep in to games. He is a servicable reliever waiting to happen if he pans out, though major leaguers may hit fly balls off Souza harder and farther than AA hitters.
Then again, Hannahan is not a huge gain. He will be in uniform for tonight's game (which probably means Josh Wilson is getting the boot), and he will likely will take most of Chris Woodward's playing time at third. Hannahan is a good defender, but not much of a hitter, and at 29 years old that's who he is going to be.
This is not as exciting as the Betancourt deal yesterday, or even the one for Ryan Langerhans. However, Hannahan is an upgrade over Woodward. Also, Hannahan and Ronny Cedeno combined are probably about as good defensively as Beltre and Yuni were, so the defense overall is back to what it was.
Offensively, this may not work out so bad either. There is no doubt that Adrian Beltre is a far superior hitter to Jack Hannahan when healthy. But, with the bum shoulder, Beltre's OPS was a very replacable .665. Hannahan's career OPS is .659, though he's not even close to that low standard so far this year.
The point is that Jack Hannahan is no long-term solution, but he's a cheap one right now. Moreover, he may come surprisingly close to replacing what was lost when Beltre went down, thanks to other moves the M's have made.
UPDATE (6:21 PM PDT) - It's Brandon Morrow going down to Tacoma to make room for Hannahan. Morrow looked real bad last night against Texas, and he may finally get the chance to work on his secondary pitches. The M's only need four starters for a couple weeks after the all-star break, and were planning to have Jason Vargas work in Tacoma to stay fresh. Perhaps they call Vargas back up, and hope a few starts in Tacoma are enough for Brandon Morrow to find a feel for his off-speed offerings. I'm sure Wakamatsu and Zduriencik will say more about the move.