Hi,
It's kind of possible.
I think you should be able to do that with a mass action:
www.hikashop.com/support/documentation/167-massaction-form.html
With a trigger "on after order updated", you could have a filter "order column" (for a custom order field) or "user column" (for a custom user field), and actions "update the values" on the columns "order_invoice_number", "order_invoice_id", "order_invoice_created" to empty their values.
That way the system would generate the invoice but it would be wiped out directly after being generated.