Win 7 32 or 64-bit when OS partition is Boot Camp on a 4GB RAM macbook

Currently my Windows 7 OS is installed in Parallels, but I want to delete it and reinstall it on a Boot Camp partition, then map the partition to Parallels.

I'm using a Macbook 2ghz Core 2 Duo with 4GB RAM, so the processor and RAM are sufficient to support Windows 7 64 bit if only running it in Boot Camp, but Parallels only allows users to dedicate half of their system's RAM to the virtual OS, I could only give Windows 2GB of RAM, which is not recommended for the 64-bit edition.

Am I stuck with having to install the 32 bit version of Windows 7?

 

I ran the same scenario with 64-bit Windows 7 in Boot Camp without any noticeable problems when using Parallels.