The answer to this is a definite "maybe".

YouTube personality Trent Palmer tested this very question. He was actually able to glide further with the engine off than he was with it at idle. It was a very small gain, though, on the order of a few seconds extra flying time per 1,000 feet descent. The people he was with reported similar small gains with a stopped propeller. They theorized that a running engine still generates a small P-factor, which has to be compensated for, increasing drag.

It's important to note that all the planes involved in the test were STOL aircraft. Its entirely possible (and indeed likely) that other types of aircraft will have different results.

The answer to this is a definite "maybe".

YouTube personality Trent Palmer tested this very question. He was actually able to glide further with the engine off than he was with it at idle. It was a very small gain, though, on the order of a few seconds extra flying time per 1,000 feet descent. The people he was with reported different results: One guy said he glided further with the engine at idle than with it off, but, again, the difference was miniscule. So, the ultimate answer is that it depends on your exact aircraft.

Edit: My answer originally said that everybody involved in the test got the same results. I was working from memory when typing this. Having rewatched the video, I see I was wrong in that, some people got different results (which actually illustrates the point better in my opinion).