Are minerals synthetic?

No. According to the current definition, in order to be an accepted mineral species, a mineral must form naturally, it cannot be manmade.

There is an interesting debate around the exact definition of a mineral, and whether minerals that have been formed by human intervention really should be considered genuine minerals or not.

Eg. the ancient Roman mines at Laurium, Greece, where poorly refined lead and other element-rich slag nodules were dumped into the sea. Millennia of reaction with salt water caused a large variety of tiny but beautiful crystals to form in the the small gas pockets within the nodules. Upon examination it was found that a number of these were actually new minerals, and described as such, but the current train of thought is that they're manmade and unworthy of true mineral status. There's lots of other post-mining minerals, they form in many strange and wonderful places. The debate on the exact definition of a mineral continues.