The OR would change the logic completely.
Let's say the group is suppressed on the following condition:
{field A} = 'A'
When this formula evaluates to True, the group is suppressed and you'd want to disregard such records from the summary calculation.
So, essentially, you'd want to sum up records where {field A} <> 'A'. So, the formula becomes:
If
{field A} <> 'A' then {measure_field}
You can then insert a summary on this formula field and place the summary on the Group Footer and the Report Footer.
-Abhilash