I don't see why you couldn't implement a POC. Can you please elaborate your question on dividing up cycle times? Which cycle times are you talking about, and why do they need to be divided up?
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
When I think of a POC (proof of concept), I think of prototypes, or lets do some coding to see if it works. Why would you write it up first, rather than just doing it? Can you explain a little better? POCs are a big part of agile. Before spending a lot of time planning something that might not work, create a story for a "spike" or POC.
I have the same questions about cycle times that Ilja had.
Co-author, with Lisa Crispin: Agile Testing: A Practical Guide for Testers and Agile Teams (Addison-Wesley, 2009) www.janetgregory.ca