Hi there. It's possible but very unlikely. Essentially if you really stood out -- great school, great GPA, great test scores, possible Math/Physics Olympiad winner, etc. then someone may give you a shot. Places like DE Shaw will always be open to someone that is the top of the top regardless of actual background. The other angle that could work for you would be to connect with small (especially ones that are just starting up) shops -- they might be willing to give you a shot. Also, if you have strong programming, that will help. To put it another way, and I say this respectfully, a lack of programming skills will almost always work against you.
Hope this helps. Please feel free to ask questions.
Sameer