If you get adapters and plug in the NES Classic to a CRT, maybe. I'm assuming you already have the Duck Hunt ROM loaded on the NESC. It won't work on an LCD or (O)LED TV because light guns can only read from a CRT. You'll need a CRT if you wanna make it work.
Here's some Amazon links:
It is not a good device to use on a traditional television. Not ideal at least. The lowest resolution the mini will output I believe is 480i. This means 480 lines interlaced, which means the beams alernate every time a frame is drawn, which results in a flickering effect that is annoying.
The original SNES was meant to be played at 240p, which is 240 lines that are being constantly drawn. That means only every other line of frame is being drawn, constantly, which results in the black void lines that we affectionately call scanlines (technically, the lines of video are considered scanlines, but that doesn't matter).
Anyway, the only way you are going to achieve that resolution is with the use of a hardware downscaler, which are rare and cost a lot of money, and wouldn't look good anyway because the Mini's UI was designed with HD tvs in mind.
So to sum up, if you want to make the shit look as it was intended, build a Raspberry pi build. Really, it's easy (if you take the time to learn about it) and fun.
If you are like, dude what the fuck are you talking about I just want to play on a tube TV, which I commend you for, then you need to get a hdmi to composite converter.
Hope this helps.