Hi,
It's up to the implementation of HttpStack that you choose to use. If your stack supports HTTP 2.0 then Volley itself should have no trouble with it.
Foe example, there are a fair number of implementations of HttpStack atop OkHttp floating around that would likely work. Or, on recent versions of Android, HttpUrlConnection is backed by OkHttp, which suggests that you might just be able to use the built-in HurlStack if you only care about those platform versions, though I'm not deeply familiar with which versions would be expected to work (if any).
(Not endorsing OkHttp specifically vs. any other solution - it just happens to be the only library I'm familiar with which supports HTTP 2.0.)
Hope that helps!
-Jeff