It is possible but not likely as even DOT 2 brake fluid boils at 374 degrees. If you routed the brake lines in the original location and are NOT using tubular headers.
As to your cooling issues if you are cruising (above 35 mph) and the motor over heats your problem lies with your radiator (clogged or under sized). If on the underhand the motor cools off while cruising but over heats at idle you have a fan that is not moving enough air (an aftermarket flex fan, or original fixed blade four bladed fan off a six or small V8), or it is missing the ducting from the fan shroud.
A 409 is a big lock Chevy (Mark I) and produces as much heat as the 396 BBC (Mark IV) engine. As such it will require a four row copper/brass or a two row one inch tube aluminum radiator. If some previous owner dropped in a 409 and retained the small V8 or six cylinder radiator it will always over heat because the radiator is inadequate to do the job.
Further the water pump on the 409 is an open design (think paddle wheel), compared to more efficient enclosed scroll impellers used in high performance water pumps like those made by Stewart. A Stewart Phase III SBC water pump moves twice the volume of water as a stock water pump, but takes only half the power that a stock water pump draws because of the scroll impeller and a smoother high capacity casting. I just don't think it will be an option for you so the best you could do is an Edlebrock water pump which uses an enclosed straight blade.
The condition of the hoses affects cooling because as the rubber ages it gets soft and the bottom hose will collapse under suction (or balloon out on the top). Hoses and belts should be replaced as routine maintenance (something most car owners ignore until they are stranded on the side of the road).
Finally ignition timing will affect how hot the motor runs. Get it too far advanced and you can actually destroy the piston ring lands from excessive heat as the fuel charge is burnt before the piston ever gets to top dead center.