I could see Chavo Guerrero being of use to TNA in a couple of ways:
Tag Team Division - It's no secret that TNA's tag team picture, once the crowning jewel of TNA and the one aspect of their product that was indesputable as being supierior to WWE, is on life support right now. I'd go so far as to say that WWE MIGHT actually have a better tag team scene that TNA. As implausible as that sounds, that's how far the tag team scene has fallen in TNA. The current tag team scene consists of "thrown together" teams that've been paired up mostly for the sake of just putting together whacky teams and Matt Morgan & Crimson, who have no real competition at this point and are generally uninteresting as tag champs at this point. With Anarquia headed down to OVW, Chavo Guerrero could be a replacement for him in Mexican America. Chavo has had success as a tag team wrestler, can easily do the schtick of representing his Mexican heritage and is simply far more talented than Anarquia. As long as they don't have him play the exact same character as Anarquia, he could be of use.
The X Division - Like the tag team scene, the X Division is pretty weak right now. it's not as weak as it has been for most of the past 3 years but it would be if not for the presence of Austin Aries. He's the only guy keeping this afloat. Would Chavo bring a new dynamic to the X Division? Probably not, but he does bring something to the X Division that it currently doesn't really have: name recognition. Chavo's last name is Guerrero and he's a wrestling veteran that has had exposure in WWE. Most of it over the course of the past 5 years or more hasn't been great, but at least he's had it. He'd basically be a hispanic version of Kid Kash except people actually know who Chavo is.
If Chavo somehow doesn't head to TNA, let's be honest, it's not going to be a loss for the company. I said earlier that Chavo is a Guerrero and he is. The problem, however, is the fact that his last name and the Guerrero family's contribution to wrestling in general are really all he has. He's a Guerrero, but he's not his father. He's also not Gory, Hector, Mando and he sure as hell isn't Eddie. The times in which Chavo has been the most relevant in his career have been in programs with him either wrestling against or wrestling with Eddie. Other than that, his entire career has been pretty forgettable in general. That's also including his time wrestling in Mexico and Japan, where he'd never really accomplished anything that I know of.