Dear hellokitty,
In short, yes 
The first method is a recipe for setting up an automatic Zenodo-GitHub integration we currently have in Zenodo, but in the end it can be done manually for any software repository, even if it lives only locally on your machine, i.e. you can upload a zip-ball of your software to Zenodo, provide some metadata and publish it to get a DOI (just as you would if you uploaded a paper or data).
Having said that, it’s probably the best if you make a zip-ball of a tagged release, so that the DOI captures something “complete”. Additionally you can supplement your record metadata on Zenodo with a “related identifier” (e.g. a URL) and point back to the tag on your live repository. This way anyone who discovers your software in the future will also have means to follow your live repository and find the most recent version of the software.