Good idea?

As long as the artist doesn't try to play it off as "real" I have no problem with adding elements. I often see people posting pictures of Tokyo with a photo-shopped Mt.Fuji in the background and try to play it off like it's a real scene they captured to gain internet points.

As for this image, the moon looks a little strange, but the overall theme is fine. Part of me wants it to be more interesting, but another part of me likes the simplicity in an "artsy" way.

As long as it is presented as a compsite, no problem, I really like this one.

I agree with Jordan and Timothy about composites.

"Dropping in" moons was common even in film days because it was relatively easy to do. In my experience it usually looks fake; maybe when it IS well done I don't even know it's been done.

A common issue is "two suns": the moon lit from one angle, but, say foreground rock formations or structures from another.

Another is perspective, and I think affects your image here. If you were shooting on 24 X 36mm format, you'd need a lens of about 500mm focal length for the moon to be that size. It's hard to be sure, but your landscape scene looks wide-angle, with the receding perspective on the foreground textures, the small figure and clouds. I'd have guessed it's about 28mm, and your EXIF suggests it was about that (equivalent).

With this, and the difference in brightness, this looks faked to me, and not interesting in a good way. But that's my subjective response. Many people love those moons!

I agree with all. If portraying as art then anything goes, if presenting as a representation of true facts (eg journalistic) then this is a definite no-no.
It's really up to the artist to decide what works, in my own particular view I'd like to see the moon rounder and smaller (ie more realistic).

I think this works otherwise.