If I used a Raspberry Pi model that features Bluetooth (or just plugged in a USB Bluetooth dongle) would there be any way to send MIDI data out wirelessly via Bluetooth so that my keyboard could also control, say, an iPad without being plugged in?
Samplerbox is a midi in device by nature, it does not produce midi-out/thru via software. Making the HW thru port depends on your DIY skills. You might also go for an external midi splitter before the samplerbox and other devices (I guess I would if I had such a need..).
Can I add bluetooth connection into SamplerBox via bluetooth midi connection
Sorry not possible with Linux , yet
Missing ble midi support
You can use ble WIDI dongle tobtalk midi