I have a spare hardtrail frame which is too big (20.5") for me (5'7") for riding trails. Would it make sense to build a commuter bike for me as road/touring bike frames are generally larger than MTB? Could it be comfortable to ride this frame on road? I like to lean forward on a bike and I'm a fast type of commuter.
It's a good, cheap way to build a first commuter. Throw on a pair of road slicks and lights and go to work. It will give you a chance to decide what you really want in a commuter bike. It will be able to handle bad roads and pot holes better than a road racing bike. But, it will still be heavier and slower than a bike based on a cyclocross/utility/road frame with 700c wheels.
You've got it the wrong way around. Road frames, in terms of horizontal toptube length, are significantly shorter than mountain bike frames. If it's a hardtail frame and it's too big for you with a flat bar, it's going to be way too big for you with a drop bar.
On the other hand, you might be able to put a bar with significant sweep on the frame and have it fit you a bit better. However, this would effectively shorten the stem, which may make the handling a bit twitchy.
Unless you have the spare parts laying around build-outs are expensive and always labor intensive.
It is not worth spending money on a frame the does not fit you. Road versus trail the fit is not that different. The frame fits you or not.
I had mountain bike that the shock wore out and bought a better mountain bike. I put a fixed fork and tires on it to use it as a city bike and still had to think about it. I am good with that decision but the frame fit me and the conversion was $200.