Will an older cat attack/kill a kitten?

I have a cat who is a little over 1 year old (big guy, fat, no longer a kitty.) He always gets in fights with other cats when he goes outside. He also brings in dead birds and rabbits that he kills. I recently got 3 kittens to foster, and we're keeping 2. They are soo tiny and cute. They're about 4-5 weeks old. Whenever my older cat, Tommy, sees them, he hisses and stares them done. The kittens just stand there and stare back, and their fur sticks straight up from being scared. My grandma (cat lady) said not to worry, that he won't attack. I'm worried that he might hurt the kittens. We keep the kittens locked in a room when my whole family leaves the house. Do you think Tommy could hurt or even kill the kittens?