Can't comment (don't have enough reputation).
It all depends on your pre filters too.
My RO/DI unit has a sediment filter -> carbon filter -> RO membrane -> DI resins.
If you have the carbon filter you should be ok filtering rain water through your RO unit.
Also keep in mind Ro filtering works if you have proper pressure: 60 PSI is best.
So you will need a booster pump for it.
This article might shed some more light on the bacteria removal (paragraph 5): http://www.purewaterproducts.com/articles/carbon
Seems between carbon and the RO membrane you should be fine.