Your double-negative in the description makes this a little harder to wrap my head around, but I think I get what you want.
The best way to think of this is through a conditional map of the options:
1) Cell is blank (no formula) -> Do nothing
2) Cell has a formula that returns "" -> Do nothing
3) Cell has a formula that returns a result -> Highlight
To implement this in Numbers' Conditional Highlighting, you need a blank cell (anywhere on the sheet is fine) and couple of rules, knowing that rules are run in a first-match basis:

The first rule filters out the cells that are blank - although I set the text to be italic, it really doesn't matter what text formatting you set here since the cell is blank and there's no text to format.
If we get past Rule 1 we know the cell has some formula, so now we need to check if the result is not empty. We do that by comparing its value to the empty cell (here you can see I chose cell E1, but any empty cell is fine). If the cell value is not the same as E1 (empty), then I set the Red Fill format.