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I'll not answer the question of whether Islam spread by sword or not fully, as I think a clear yes or no -as it seems to me- is a bit hard to proof. Instead, I'll focus on whether rules of Islam could have been used to force non-Muslims to become Muslims
The Islamic theology includes a special jurisprudence for non-Muslims who live within a Muslim territory. Muslims call those non-Muslims Dhimmi's ذمي or ahl-a-Dhimma أهل الذمة. (The linked Wikipedia article says a lot more than I will explain here.)
According to this, a Dhimmi is a citizen of an Islamic State who is protected by the State. Those Dhimmi's could even have their own court.
The Dhimmi status was originally applied to Jews, Christians and Sabians. Later, it was expanded to cover most other non-Muslim religions.
In some cases, those Dhimmi's have been living separate from Muslims, or were required to wear special clothes, in order to distinguish them from Muslims. (It was also the case for slaves AFAIK; for example, slave women were not allowed to cover their heads, as was usual for free Muslim women.) For example, in Morocco, when you hear a district called "Mellah", you can safely conclude that it was a former district where only Jews used to live.
Dhimmi's used to sign a contract which would fix the rules of their protection by the Muslim authorities and for this, they would have to pay special taxes. A benefit, would be that they would never have to fight for the Muslim State in case of war!
Nevertheless, local authorities (Governors, Sovereigns, Leaders) could have oppressed their non-Muslim citizens using these taxes and in this way force them to chose between:
As you might find in the linked article, the Quran doesn't fully support this. As additional evidence, I could add this Verse, which was quoted by the contemporary scholar Yusuf al-Qaradawi when he tried to explain that the name Dhimmi isn't up to date, and that Muslims should cancel it and replace it by calling them citizens and not to make differences between Muslim citizens and non-Muslim citizens (according to the Arabic wikipedia-Article).