Way back about twenty years ago when I was 21 I went from Maryland to Florida with a backpack on a cheep mountain bike.I don't recomend it cheep mountain bikes breakdown more often and backpack are ment for hiking not riding.I didn't have that much stuff in it but I was wishing that I didn't have it at all.I suggest looking at the touring section more and try to get a little more prepaired.
While it can be done it is not that much fun,bags mounted on the bike are much better than a backpack.