You have 2 options:
a. Deploy Boost DLLs together with your binary. Answering your question - of course if your project depends on Boost, the libraries are required at runtime, your binary will not start without them.
If you deploy Release configuration of your project, then you need boost_filesystem-vc90-mt-1_40.dll
library. In general you can just see all the dependencies of your binary using Dependency Walker
tool.
b. Link Boost libraries statically, in this case your binary will not have runtime dependency on Boost DLLs, so you don't have to deploy them