It actually depends on the amount of tweets with that hashtag. If the amount is really less, it might be possible. Twitter documentation mentions that -
Clients may access a theoretical maximum of 3,200 statuses via the page and count parameters for the
user_timeline REST API methods. Other timeline methods have a theoretical maximum of 800 statuses.
Requests for more than the limit will result in a reply with a status
code of 200 and an empty result in the format requested. Twitter still
maintains a database of all the tweets sent by a user. However, to
ensure performance of the site, this artificial limit is temporarily
Add to that, the search API's
page parameters says -
The page number (starting at 1) to return, up to a max of roughly 1500
results (based on rpp * page).
So that would mean that Twitter doesn't intend to give back All the data it consumed. It'll hold back some. In that case, you cannot do anything, unless you find a third party service that indexes tweets.
The best bet if to try searching combining the
until parameters and see how far you can go.