L-38,
JMHO's here; your hypothetical question "would they keep running at take-off power is problematical at best.
I had a classmate who was let go because he believed the ground school teaching that "suction" fuel at climb power would work with boost pumps off and the crossfeed closed. He was arguing with the mechanic on the jump seat about whether or not it would keep running, so he decided to show him by killing the boost pumps and closing the crossfeed (i.e. isolating the engine from a pressure fuel source.)
The engine quit before under something like FL180 so: he lost that argument.