Can LEGO Boost play custom audio files?
As far as I can tell, recordings from the tablet are the only way to use custom sounds at the moment. I imagine that the UI for a feature like this was deemed too complex for an app designed for children under 12. However, this should be easy to add to the app in a future update if there is demand for it.
One obvious workaround for this is to play the desired sound on another device and save it using the recording interface:

These recordings are limited to about 5 seconds.