SmartThings has no Bluetooth capability yet
The shortest answer is no, not as you describe, because the hub cannot detect Bluetooth at the present time as its Bluetooth radio is not enabled.
Also, there’s a security feature to the Bluetooth protocol – – you can’t have just any device listen and react to it. They have to be paired together. That’s why it matters that the Bluetooth radio in the hub is not enabled. If it were enabled, we’d presumably be able to pair devices to it and we’d have a lot more options.
But wait-- an android phone could act as a man in the middle and capture the Bluetooth events
The longer answer is yes, just use an android device, pair it to the button, have it detect the Bluetooth event, and use a combination of Tasker/sharptools to tie it into smartthings. A number of community members use this with all kinds of different Bluetooth devices including the satechi button. @joshua_lyon could probably say more about this option.
See for example:
and some Bluetooth devices, like flic buttons, come with an android or iOS app that can capture the Bluetooth event and communicate via IFTTT
And the medium answer is that there has to be something that can be paired to the button and recognize the Bluetooth event when the button is pressed. If the Bluetooth device talks to your phone and the app that captures it is able to communicate either via Wi-Fi or with IFTTT, again, super easy. This is exactly how people use Flic buttons with smartthings. This method will work with either iOS or Android because the key is that the receiving app already knows how to then talk to IFTTTT or harmony or your Wi-Fi. Many Ibeacons, which use Bluetooth, also have apps that run on phones or tablets that can use the IFTTT maker channel. But there’s no general answer for this particular approach, it just depends on each receiving app.
Summary
So with android you can do it with most Bluetooth devices. With iOS, you can do it with those devices that come with an app that has external communication abilities, particularly to IFTTT.
(by the way, to answer one of your questions, almost all Bluetooth button devices activate only with the button press – – otherwise they’d run through batteries too quickly. The receiving station, though, is usually always on, but that’s why that’s typically a phone or tablet.)