If I get it right you can just add a window function outside of your query like:

SELECT interval_date, campaign_revenue
     , SUM(campaign_revenue) OVER (ORDER BY interval_date) 
      + (SELECT SUM(revenue) 
         FROM sale_event
         WHERE s.campaignid = $1 
           AND s.event_type = 'session_closed') as total_campaign_revenue
FROM (
    SELECT interval_date
         , coalesce(campaign_revenue,0) AS campaign_revenue
    FROM
        -- generate_series helps fill the empty gaps in the following JOIN
        ...
        interval) results
    ON (results.interval = interval_date)
);

Another option is to apply the window function directly, and use a FILTER clause for campaign_revenue

If I get it right you can just add a window function outside of your query like:

SELECT interval_date, campaign_revenue
     , SUM(campaign_revenue) OVER (ORDER BY interval_date) 
      + (SELECT SUM(revenue) 
         FROM sale_event
         WHERE s.campaignid = $1
           AND s.created < $2
           AND s.event_type = 'session_closed') as total_campaign_revenue
FROM (
    SELECT interval_date
         , coalesce(campaign_revenue,0) AS campaign_revenue
    FROM
        -- generate_series helps fill the empty gaps in the following JOIN
        ...
        interval) results
    ON (results.interval = interval_date)
);

Another option is to apply the window function directly, and use a FILTER clause for campaign_revenue