I dont think it will cripple you but consider this:
Most successful MD/PhD applicants not only have research experience, but the quality of their research is very, very good. These people did not just spend 3 years in a lab doing basic procedural stuff. They were forming their own experiments and working quasi-independently within the lab.
My point is that being a non-science major will make it harder for you to engage in such original research because you wont have the in-depth science background like the others do. Now, its possible for you to work at their level, but you will have to read and study ALOT on your own to compensate for the lack of advanced science training that you wont be getting.
You can do it, but just keep in mind that working in a lab is not good enough to get admitted to MD/PhD. They look STRONGLY at the QUALITY, CREATIVITY, AND ORIGINALITY of your OWN research conducted while in the lab. Just spending 3 years working in a lab mixing chemicals is not good enough.
It will help set you apart from other MD/PhD applicants, but just remember to engage in orignal research as much as possible instead of just following existing protocols.