My wonderful neighbor behind me uses a gas mower every Saturday. Three weeks ago, I started letting my chickens free range in the back yard, and he, apologetically, said he had to mow his yard, but would make the passes by the fence between us with the exhaust only on the side away from my yard. In other words, he wouldn't do the turn-around to come back "the other way," but make the next passes there after doing other rounds. But he would still have to run the mower by the fence.
At the time he asked, all my chickens were happily scratching right along that fence. They scattered when he started the mower, but afterward just acted like nothing was going on. Their run is only a few feet away from that fence, and he's mowed his yard every Saturday. I guess they'd gotten used to it; that noisy thing never came into THEIR space to harm them....
Some of my girls were really interested when I was building the new coop, and the sound of a circular saw and/or jig saw never fazed them in the least. (To my surprise.) I even had to move my work area OUT of their run, because they'd hop up and want to look really closely at the spot where the sawdust was shooting out!!!! Idiot birds.
I think yours might be startled at first.... and if they're young, might panic some. But I don't think they'll have heart attacks... They WILL love the bits of grass left behind the mower!!!