er....no. China had well over double Europe's GDP in the 1200s. even more so after Black Death ruined Europe.Europe's estimated GDP had caught up with China by 1200.While these are modern estimates,medieval Europe was not backward or poor.
Europe wouldn't catch up with China's GDP until roughly the early 1700s with the devastation caused by the Ming-Qing wars...and ironically the weakening of the Ming was partly due to the massive inflation caused by the influx of Spanish silver from the New World. roughly 40-50% of all the silver in Mexico and Peru that Spain stole from the Incas or dug up with slaves ended up in Ming coffers.
shortly thereafter, the mid-Qing economic/population boom left Europe in the dust until roughly the 1830s with the Industrial Revolution. it wasn't until the chaotic wars of the 1850s-1860s in China where European economy exceeded China's.