e.g. When you and I log into ff, simplifying greatly, that page would say, "Welcome, Bret" or "Welcome, Prakash". If you could abstract away "Bret" and "Prakash", that page would be cacheable. And, the db hit is only for that particular fragment.
You would need to re-code the pages with esi tags to do it. The other way would be to use javascript to do the same.
Suffices to say, no, we do not support that :)