I don't think they're trying to recruit Ellie, although the way the last episode ended, that route makes sense. I think they're trying to recruit Chuck.
He took out Shaw, so he must be a big deal in the spy world by this point. And if they can get some leverage (like forcing Chuck to save Ellie/Awesome, his dad in the upcoming episode, or Sarah), Chuck would always sacrifice his own ambitions to save someone else because that's how he rolls. Plus, the dude has the Intersect, and it's pretty valuable to keep him alive for that purpose.
Next episode is going to make it look like the Intersect is messing with his brain, and that's why they need to bring in his dad to "fix" it. I wouldn't be surprised if this season ended with a "will he join the Ring" cliffhanger, and then it gets resolved with a simple "no that would be bad" resolution if it gets picked up for a 4th season.
Based on this week, they're recruiting her to get to her dad. I'm curious how this is going to play out - it looks like this will be the show's way of "outing" Chuck to Ellie. I get why they kept that in place, but I always felt like it was a little bit of a stretch that he wouldn't tell her, especially once Awesome found out.
Yeah now that everyone and their dog knows that Chuck is a spy, might as well get Ellie in to the loop before anything else happens.
You'd think that she would tell Awesome about the "doctor" who is actually CIA... seems odd that she would just take his word for it and then not reveal that info.