With Alvarez inside, Garrett Atkins stepped in at third base during defensive work with the rest of the starting infielders. That gives you some idea of the initial depth chart.
Whether or not Atkins will make the Opening Day roster is a question upon which I can only speculate, and it's surely possible he's getting reps with the starters because of his relationship with Clint Hurdle. But it wouldn't be surprising at all if the Pirates considered him a favorite for a bench spot at this point.
I'm open to the possibility that Atkins could recover some portion of his 2006/2007 form, but it doesn't seem likely - ZiPS thinks he'll hit .248/.307/.373 (although that's a prediction for if he were playing with the Orioles, not with the Bucs). If he makes the team and hits like that, well, he'll belong in a class with recent Pirates veteran acquisitions like Jason Michaels, Craig Monroe and Ryan Church. (Okay, he'd be a bit better than Monroe or Church. But not by much.)
The only advantage Atkins has over potential bench players like John Bowker and Steve Pearce is that he can back up at first base and third base. As bench infielders go, however, that doesn't exactly make him versatile, especially since he isn't much of a defensive third baseman. ZiPS projects Bowker to hit .264/.329/.430 and Pearce to hit .254/.326/.434.
I liked Atkins as a minor-league acquisition, and he'd be fine to have in Indianapolis, if he doesn't have an out clause in his contract that allows him to leave if he doesn't make the team out of Spring Training. As the default candidate for a bench job, though, he leaves a lot to be desired. Three bench spots will go to Matt Diaz/Garrett Jones, Ryan Doumit, and a utility infielder, perhaps Josh Rodriguez. That leaves two. If you want fielding ability, Ciriaco is a better option. If you want versatility, there's Corey Wimberly (who admittedly projects to hit very little). If you want players who can hit, Pearce and Bowker appear to be clearly better. Even if, for some reason, you just have to have a guy who plays third and first, Josh Fields and Andy Marte are younger than Atkins and aren't obviously worse.
Like I said, I'm open to being wrong here, and even if I'm not, having a bad veteran at the end of the bench is just an annoyance, not a huge problem. But there are lots of guys on the depth chart who should be ahead of Atkins right now.