Firstly realize that Sapir-Whorf was proven wrong in the strong sense, but is accepted in the weak sense. I don't think there's really any doubt now that learning new symbols and languages, or just enhancing your vocabulary in one language, influences thought. Many mathematicians are especially proud of how accurately proofs communicate, and having gained this accuracy, the mind comes to expect it more and loathe ambiguities. You see this happen with a lot of people in quantitative disciplines.
There doesn't seem to be a lot of research, but you're not the first to think of it. Many programmers before have too (see wiki's references):
Of course, none of them were neuroscientists or psychologists. To test for causality would be difficult to control for (you'd have to provide a mechanism and we're only just about getting there at the neural systems level). On the other hand, I'm sure you would find a correlation between programmers and certain kinds of behavioral and cognitive traits very easily.
In the end though, I don't really think there's any doubt among neuroscientists or psychologists; it's just a matter of finding the neural mechanism. Language has been a pain in that regard.