I think it would be hugely beneficial to already have completed the ROUTE/SWITCH curriculums before studying ARCH - after all, this is all about learning. When you take the test is up to you.
The ARCH exam is going to cover a LOT of topics, that aren't just route/switch, from a design perspective. This includes route/switch, but also includes security, load balancing, storage networking, etc.
I strongly recommend doing ROUTE/SWITCH first. They aren't absolutely necessary, but I think you'd gain more, and learn quicker, going in with that knowledge base already developed.
I agree with Travis. Routing and switching are some foundational topics for other subject matter, incuding design, including load balancing and the like. If it is the CCDP you are interested in, I would actually suggest that you complete the CCNP, if you haven't already and then do the ARCH exam to complete the CCDP. The CCNP, in my opinion, will give you some foundational info that will fit in nicely to the CCDP.
I have personally found the same concept to be true with the CCDA and the CCNA Concentrations. It sure helps if you have some background knowledge in Security, Wireless and Voice for the CCDA because the CCDA also covers a lot of topics.