You can connect, as long as it is not induced on the 12V VF line, so nothing should happen to the radio, but to be sure, I would put a couple of 16V transils on the output in parallel and I would at least thread the cables through a couple of threads through a larger toroid. Induced HF to the power supply from the TX can cause an increase in the output voltage.
You have to find out for yourself if and how much the RX will interfere. That source is not built for KV radio.