Hi BritGeek!
Can you use Web part connectors to refresh the list web part?
Another idea would be to create a separate InfoPath form inside an InfoPath Web part and to use this instead of the stock list web part. Then you can use web part connectors between the two InfoPath web parts to refresh one another.
So, yes, I believe it's possible so long as you are using an InfoPath form with a rule and a list query to display the data. When the input web part value changes, just requery the list and the InfoPath dashboard web part will display the refreshed data.
We're doing a webinar next week (Thursday at 8am Pacific) on how to use InfoPath as a SharePoint dashboard design tool - i.e. not for forms, but for displaying SharePoint data. Highly recommend you join us for that.
We love you for using qRules!
:)