This might seem like a dumb question but..

You know how the major scale has certain degrees, especially the leading tone wanting to resolve into the tonic. Well, what about in a natural minor key? For example, A minor. The G note in A minor is a whole step from the root note ascending and lacks the desire to resolve into the tonic ( music theory . net) . Does this mean that it would sound weird if you kept resolving from G to A ? Or can you basically just treat the scale degrees characteristics in a natural minor scale the same as a major scale.
I think if you really wanted to build the kind of tension you're talking about here, you would use a G# anyway. My reasoning for this, is that when you want a V chord that will resolve into a minor, you use a V7(b13,+9,b9), which has a major 3rd. The major third of the V of the minor tonic 1/2 step below the tonic.

Sorry for the convoluted response, that's just what I think.

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If you leave the 7th natural in minor you'll get a modal sound (in classical harmony at any rate. In popular music, the seventh is often left natural and "resolves" to the tonic). If you're talking harmony though, you will always raise the seventh when leading to one to create tension and resolution.
You could still do it and it'll sound fine, it just won't sound as resolved as the leading tone would.