The GetSelectedCount function will tell you how many items are selected in a certain field.
GetSelectedCount(FIELD) > 0
If you have multiple fields, then you can combine them:
GetSelectedCount(FIELD1) + GetSelectedCount(FIELD2) + GetSelectedCount(FIELD3) >= 3
You could also put this as a Calculation Condition. If the Calculation Condition is not met, the chart outline will display, but there will be an error message and no data. The error message can even be customized. This may work better as you won't have a big blank space in your app.
Not sure how to do exactly what you're asking for other than exhaustively checking every possible field, but what about counting how well their filters have narrowed down the data set? Something like count(MainID)<100000. It'll still take a little time to do the count, but probably nothing like the chart, assuming you have a complex chart.