A few days ago, there were a couple questions on buffer overflow vulnerabilities (such as Does Java have buffer overflows?, Secure C and the universities - trained for buffer ov
I don't think so.
As I see it, instead of programming paradigm, vulnerabilities like buffer overflows has more to do with the compiler/interpreter architecture/virtual machine.
For eg, if you are using functional programming in .NET environment (C#, VB etc), as long as you are dealing with managed objects, buffer overflows will be taken care of.