I don't know if this is possible or makes sense to do anyway, but I was thinking - could I somehow add my netbooks processor to another computer to act as an external core for better performance on the primary computer?
In the general case, no, clustering is generally only good for running applications designed to be run on a cluster. There are issues with dividing tasks across separate nodes (latency is a non-trivial factor) that simply aren't considered in most desktop applications.
There are some tasks / applications that do implement support for this. If you've got a specific task in mind you might benefit from doing some looking around. Examples that come to mind are:
Both are very much limited to specific domains, but other examples probably exist if you wanted to do more research.
Is there a specific task you're trying to speed up?
Short and simple!
Even if you use a multi processor motherboard, I have seen none that support anything less than a server class (or very high end) CPU - such as Xeon or Opteron.
... The closest thing would be using it as a separate machine for programs that are capable of splitting workloads such as rendering, however the improvement of using an Atom (guessing) would be marginal.
Early supercomputers used parallel processing and distributed computing and to link processors together in a single machine. Using freely available tools, it is possible to do the same today using inexpensive PCs - a cluster.
more here: The "Mini-Cluster"
In the early 90's there was the concept of a "Maths Co-Processor" that was a plug-in chip for cheap 486 SX's and that kind of era. It was a dedicated chip for doing floating point maths if I remember correctly, and the cheap SX did not have this by default. The better DX did.
That said, that was almost 20 years ago, and no such thing exists today.
Plus, a netbook's processor is hopeless at almost everything except browsing the web and chatting on facebook. I doubt you would get any additional benefit out of it even if you could link/cluster it.