I doubt it. It seems to me that this American Life was responding to the fact that patent trolling was already very much on the radar, not putting it there themselves.
But given this has been an issue for so long, why the action now? Did TAL raise something as an issue that motivated folks to call their congressmen, petition their representatives more than if TAL had not aired the episode? If it's just timing on the part of TAL, it's well timed.
Don't get me wrong, I love This American Life, but a week before the more recent episode aired the State of Vermont passed a law to clamp down on patent trolls and its attorney general started suing patent trolls. See: http://abovethelaw.com/2013/05/vermont-declares-war-on-paten...
Obama made statements in February regarding the harm imposed by patent trolls: "On a Google Hangout in February, Obama said patent trolls abuse a system that was designed to protect inventions and foster innovation. "They don't actually produce anything themselves," Obama said. "They're just trying to essentially leverage and hijack somebody else's idea and see if they can extort some money out of them." (http://money.cnn.com/2013/06/04/technology/innovation/obama-...)
Also, the This American Life episode just aired last weekend. I highly doubt the executive orders were written in one business day.