That sounds reasonable, but if you scratch the surface, it falls apart. Jews didn't control any trade. They engaged in the trade they were permitted to. Muslims & pagans controlled the routes to the East. Christians controlled most of Europe.
It's true that Jewish communities existed all over Europe Africa & Asia by that time, but they were heavily persecuted, relatively isolated & the vast majority were quite poor.
The idea that Jews were/are "usually rich money lenders and traders" is an old, old prejudice. Today, it's been modernized into statements like "Jews control the media" or "Jews control the government," but it's really just the same old song & dance. If we controlled the banks, media & government, I wouldn't be working my a$$ off every day to support my family...
In Christian Europe, Jews were forbidden by law to own land & practice many trades so they were left with being merchants, jewelers & money lenders. Christians were self-forbidden from practicing usury so Jews, who were outside Church authority, filled the need. Even the nobility needed a loan from time to time, but if, say, one took out a loan & then announced that the plague was caused by Jews poisoning the wells...there wouldn't be anyone left to repay when the riots were over. As far as I know, the Templars were the only Christians given permission to practice usury back then & even they got rounded up & executed in the end. It was easier than paying back the loans.
Life was much easier for Jews in Islamic regions, but there was persecution there, too. One law forbade Jews from riding on camels so that a Jew's head wouldn't be higher than a Muslim's who might be on foot or horseback. To this day, Sephardic & some Ashkenazic Jews sway as if riding on a camel while praying as a hidden protest to that one. If anyone asked, they'd just say they were bowing to G-d. Despite things like that, Judaism had a golden age under Muslim rule in Spain & there were periods when Jews did very well in the Ottoman empire, even being granted titles of nobility.
My point is that Judaism didn't offer any political or economic advantages at all over Christianity or Islam during the Middle Ages. The only reason most of us have even heard of the Khazars is the fascination of their leadership adopting Judaism when & where they did. It can't be shrugged off by just saying that Jews were rich.