Our company uses public folders extensively and we think an onsite exchange server gives us a big advantage in speed of e-mail maneuvering too. However we don't have a generator backup power system and in Florida power outages from storms in the summer can last 2-3 hours which forces a server shutdown and of course loss of e-mail. Is it possible to have hosted exchange company e-mail to retain e-mail during these outages and also keep an onsite exchange server? Can I retrieve my company's e-mail from the hosted exchanger server by downloading it to my onsite exchange server? Is this simply called bagging or would one use some modified POP retrieval of e-mail from the hosted s

There are alot of companies that offer message continuity as well as spam/av/email gateway features out there.  I would suggest taking a look at them, looking at what they offer/price and choose the one that works best for you.  I don't know your company culture or business requirements so I really don't want to recommend one over the other, but some examples of these that I have had some experience with are like Mimecast, MessageLabs, Postini.  I think Exchange Online Protection might do some of this well, but I don't have any experience with that.

https://technet.microsoft.com/en-us/library/jj200581(v=exchg.150).aspx

This outlines the hybrid installation procedures for exchange. I will follow accordingly. Thank you all for your help.