The overflow is very active. I used to think mine never even worked. That was until I swapped it for a very small, but pretty, chrome tank. It is WAY more active than I ever imagined.
With 2 gallons of coolant in the system, the little in the overflow isn't hurting anything. Again, if all is well, stat is working and not stuck, hoses are good, not loosing any to boil over, even if cap is welded shut, the system will do what it wants to do and add/draw coolant as needed.
Don't worry about it and find something else more worthy of the extended efforts.
JMHO however that is exactly what I would do/am doing on my Durango. And I think itis getting along just fine.