You can totally get by using your Tele with the right impedance matching (as pointed out by Mac), and some fender amp simulation in Sonar. Whether or not you can play chickin' pickin' style is up to you.

Spring reverb simulation is of course necessary as well, if you are going the amp sim route.

My favorite chickin' picker is a guy out of south Florida, Lefty Jay Smith from Florida. He has a version of Hot Rod Lincoln that just rocks. Here's one of his YouTube videos with some chickin' pickin'-like stuff.

https://www.youtube.com/watch?v=EcXN_aam1S8

If you have the tweed around, put it to some use!

If not, you can get there with amp simulation.

-Scott