Various iMac web pages refer to or describe modifications to the iMac logic board that purport to support an external display or other non-iMac compatible external peripherals. What impact would these modifications have on my warranty?

Modification of your iMac logic board, or any other Apple board, voids the Apple Limited Product Warranty for that board. Accordingly, you can expect your service provider to charge you for service to that board, if it requires service after modification.