Yes, the quran, hadith, sira, and sunnah all encourage jihad by the sword.
This is even more obvious when you learn of naskh/abrogation and learn which verses came last and abrogated the most earlier verses.
The hadiths, sunnah, and sira merely serve to nail the coffin shut on the topic.
The bare bones of the pro-terrorist view of the islamic teachings, as I understand it, springs from the fact that in the holy texts of islam, EVERYONE is born as a muslim - so those who are not currently muslims have apostatized, and apostates under sharia can never be considered innocents, so the death of non-muslims is perfectly ok.