There is some truth to that. If possible, you might be able to find the book at your local library. I don’t buy books anymore so I discovered this one at the library. I’ll give you a short synopsis/summary of The Great Arab Conquests by Hugh Kennedy.
In areas like Syria, Israel, Lebanon, the Arabs (and there is a difference) came in and basically said pay us or die. They decided to pay though there were battles. Force was used but I can’t remember details so I won’t speak to what I can’t remember. There is an account by an Orthodox monk about the conquering of Syria (I don’t remember the place for sure) and about how the Arabs acted.
There’s several accounts of the conquest of Damascus that argue over which gate the Arabs had gone through and if they had surrendered before or after the Arabs had entered the city (before meant they only had to pay tribute; after meant destruction, death, or the “offer” of conversion). They set up a mosque in a part of a church, left a garrison, and left. Did that up and down the Mediterranean seaboard.
In cities where there was a Jewish population, the agreement that the citizens in the city made with the Arabs was to kick all the Jews out of town and if they didn’t leave then they were to be killed. They also did this with other groups. They made that agreement a lot (unfortunately it came from an agreement the Christians had made with regards to Jerusalem). The Arabs left the infrastructure in tact and left a garrison in place to keep the peace. The area had been under so many different occupations over the centuries that a new occupier was not that big of deal at the time. Syria became the home of rich Arabs (trade routes were largely based there) and so more and more converted.
Arabs didn’t want people converting to Islam because that would mean the tribute and money would dry up. Arabs went out on conquest for booty (of the pirate variety) because there wasn’t anything at home for them.
Iraq converted and so did parts of Iran after the destruction of the Sassanians. There was force used in these regions. The Berbers in Northern Africa were the largest group to convert but they did so of their own freewill.
Eventually, about a century after Muhammad died, the situation was so bad that if you wanted to survive or have a job or eat, being a Muslim was the only way possible. The corruption of government had gotten so bad and the taxes so high that being a Muslim was the only way to live.