tl; dr: no, I do not believe that Volley should send If-Modified-Sinceas part of its requests, at least not in the way it does now.
Longer answer:
Volley If-Modified-Since, Date .
, , , (.. Last-Modified).
, 200 Volley/Android:
Request 1
If-None-Match: "cd090c6cb990a25585f1748d85d764bd"
If-Modified-Since: Tue, 16 Dec 2014 14:21:13 GMT+00:00
Response 1
ETag: "cd090c6cb990a25585f1748d85d764bd"
Date: Tue, 16 Dec 2014 14:21:29 GMT
Request 2
If-None-Match: "cd090c6cb990a25585f1748d85d764bd"
If-Modified-Since: Tue, 16 Dec 2014 14:21:29 GMT+00:00
Response 2
ETag: "cd090c6cb990a25585f1748d85d764bd"
Date: Tue, 16 Dec 2014 14:23:31 GMT
Last-Modified, http- If-Modified-Since... Volley If-Modified-Since Date .