They don't have to, but if you are being stealthy, they can glide for quite a while.
They didn't always shut them off or silence them but that was the only times I was able to see them as they fired on the range.
There is no mistaking that sound when they use the main gun.
I was on my duece and a half out near the range.
The F15's would keep their distance, but the A-10's were right there close to the ground.
It was awesome.
Trust me, they're never shutting off the engines in flight. Too risky.
Those turbofans are pretty quiet though compared to what you'll find in F-15s, etc.
The A-10 actually has a feature in its engines separate from the same engine installed on the S-3 to help keep it lit when it sucks in exhaust gases from the gun.