With my demonstrated mod of epoxying a cap to the output side, yes this is now a closed system...closed to anything going in other than clean water from the filter, and closed to air coming out.
If you use soft bottles as I do (platypus, evernew, etc) you simply start with all the air squeezed out of the clean bottle. If I want to fill the bottle to the absolute top and have not done a very good job of squeezing out all the air to start, I sometimes have to slightly loosen the cap at the very end of the fill.
The only way for this closed system approach to work if you use hard bottles (Nalgene, SmartWater, recycled PET, etc) is to leave the cap slightly loose to allow air to escape. IMO this is still a vast improvement as you only barely crack the cap open. For anything to go in from outside the system, it would need to do so past the air coming out.