Right, that will work for the badge definition, so for any future awarded badges it will reflect that. That may be all you need in your situation.
But already awarded badges also will have their own expiration in the expire column of the badge_issues table.
And once a badge is "baked" with the metadata and downloaded that data is set in the image. So already awarded badges living out there somewhere in emails or backpacks etc will not have the updated expiration dates.