Unfortunately, that probably won’t work because the hue bridge does not send information about its accessories (the Hue dimmer, the motion sensor, and the Tap Switch) to SmartThings. Just the bulb status.
There is an Osram lightify dimmer switch which looks different than the Hue Switch but has a very similar purpose and will work with SmartThings. It’s also battery operated, but is made to be installed over the top of the existing power switch. Although you can also just mount it anywhere on the wall that you want. There’s a community created device type handler that works well with it.
(For whatever reasons, this company keeps changing its marketing name. Osram/Sylvania/Lightify/LEDvantage are all the same and you may see an individual model listed under any of those.)
You can find a device type handlers for it on the quick browse lists in the community – created wiki in the device type handler section on the “lighting” list. There’s one handler that let you use it like a button controller so you could also have it controls zwave lights or run a routine or whatever. And one handler that assumes you were only going to use it to control zigbee lightbulbs and you will bind those bulbs directly to the switch. They’re both good, they just have different uses. The button controller one give you more features, the zigbee only one may be a bit faster.