If I save my custom campaign draft, will the filters I selected save as well?

Yes! Any filters that you have selected will be saved when you click "Save Draft."

Replicating a campaign will also produce the same filters from the original campaign.

While the filters remain the same, your list of recipients may change depending on when you are working on the campaign. Filters will always yield a list of recipients that fit current conditions. 

For example, let's say you previously saved a campaign draft using the filter "unscheduled patients who are past due for a recall by 0 to 3 months." When you return to edit the campaign at a later date, the list of recipients will reflect whoever currently matches that filter.