AFAIK It is not possible ATM, but we were considering adding that feature when we move from python-nose to PyTest [1].
Hmm, maybe it will be possible using the export / import feature, but will probably need some custom code for it.
So you'll run basic suite, get your env up and running and then export it to a tar.gz file. next time you want to test something, you import it back and run only the test you want.
We've been working on a project called 'ovirt demo tool' [2] which will officially replace ovirt-live using Lago images, it is still under development, but should work for basic suite if you want to try it.
The manual job [3] should also allow saving the run as an image as an option [3], by setting the 'create images' option to 'yes'.