Only a few of them work, drop shadow, inner glow, outer glow, for example. If you want something more complex such as an emboss you will need to create it by hand, but it’s fairly easy, you can get away with it by adding additional fills to your main object and varying the opacity, then add a blur and displace it to one side, the other one should be displaced to the exact opposite direction and filled with the opposite color (i.e. black and white).
In my own experience dragging and dropping works better when it’s done from Illustrator to Photoshop, but not the other way around, it’s always to link photoshop files via the file>place menu.
Also if you google emboss in Illustrator you will find several ways to do it.