In the impossibly slim chance Ryuk actually did this would it have killed him like Rem?

According to the previously established rules, yes.

Only if it would have saved his life.
I don't remember enough of DN to know if that would have happened or not.

>>280881035

Pretty sure the plan was to put Light in a cell for the rest of his life rather than execute him. The gunshot wounds probably wouldnt matter, the spk and task force guys being alive or not isn't really relevant because they'd treat him so he could make it to prison.

Only if ryuk had feelings for light, with "feelings" having a very broad meaning. Rem agreed to kill L before Misa was caught the first time, and she said he could kill L because she "didn't like Light, so even if she prolonged his lifespan she wouldn't die". Later, when Misa was kept prisoner, she admitted she couldn't do it anymore because she started to feel sympathy for Light, and that would have been enough to kill her.
Ryuk found Light very entertaining, but I doubt he felt actual sympathy for him as he didn't hesitate one bit to kill him in cold blood as soon as Light couldn't provide any more entertainment to him.