No, I have not been able to make it work that way.
The workaround I use is a two-step form. I add the connection field that I want to set in the first step of the form and hide that field on the form, then make a rule to set the connection field, and then change the submit rules to go to step two of the form.
Typically, I won’t add any other fields to the first step and just rename the button to something like “Create new Invoice” or “Start Quote” so that it doesn’t seem like a two-step form.