As others have said, the Z wave devices will not work. Zigbee devices are OK if they are not “amplified” as the US allows a power transmission level of almost double that of the UK maximum, so amplified zigbee devices are not legal there.
SmartThings senior staff have confirmed that for 2016 The SmartThings branded zigbee multi-sensor and motion sensor should be OK, but the US version of the water leak sensor uses amplified Zigbee.
All of that said, whenever you’re buying any electronics outside of the UK and the EU, check the label to see if they are certified “CE.” If not, they might be seized by customs on your way back in. This is rare, but can happen especially if you appear to have a large number that might be intended for resale.