If you get all the water out you maybe safe with black and gray holding tanks the problem is, is it all out around the knife blades in pipe drains. As you pour RV-Anti down for traps some will get to the blade areas just make sure you add a little more to be sure, its cheap insurance.
As Homer says I wouldn't add to fresh water tank your tank should have a low point drain that will get most of the water out.
Heres a LINK
to help with any other questions you may have if not keep asking its better to know than have problems next spring.