Good question! According to answers in these two posts it's not possible.
I'm surprise that the binding's Enabled property isn't available in script.
A possible work around is to put an IF statement into your query's WHERE statement and pass in the query "enabled" as a QueryString variable. In MySQL it looks like this:
SELECT <field1>, etc.
FROM <tablename>
WHERE IF({enabled} = '1', id > 0, id < 0)
I tested this by binding to a toggle switch with this binding:
if({../ToggleSwitch.props.selected}, '1', '0')
In your case you might need to create a property on something with an expression that somehow detects that the dropdowns have been populated.
The binding will probably run once on view load but should be quick if you use a primary key in the IF statement. It will then execute again when the {enabled} querystring turns on.