For your system -- NO the only real reason to update to a 64 bit OS would be if you are running more than 4GB. of system memory -- since 32 bit OSes have a limit of 4gb. of addressable memory space to use more than that you need a 64 bit OS --- in your case with only 2GB. of ram you have no need to change to a 64 bit OS and doing so will provide no benefit at all (Unless you plan to add more memory later as well) and truthfully sticking with XP and saving the OS upgrade money toward purchasing a new system in the future would probably be your best bet since any money you spend on it is pretty much wasted when it comes to performance benefits and that $100 will be much better spent toward a new system sooner.
You only need 64-bit if you're going to use a system with 4GB or more of memory. If you're buying a 2GB system then you don't really need 64-bit Windows.
BUT - if you end up running programs that use up that 2GB then a memory upgrade is by far the cheapest and most effective way to boost performance. And you won't be able to benefit from the full effect of an upgrade to 4GB unless you have a 64-bit version of Windows.
So if you think you may upgrade memory to 4GB or more during the lifetime of this system, then IMHO it would be wise to install 64-bit Windows now rather than going through the pain of having to reinstall it from scratch later on.