No, it does not supply power across all 3 phases in a blackout. Nor does it (necessarily) have to backup everything you have on one phase, which is what I had initially assumed.
Instead, you can nominate one or more circuits as the "backup loads" to remain powered in the event of a blackout; for example, one or more light circuits, kitchen, etc. Consequently, these will all be on the same phase.
As a simplified explanation, from your main supply meter / switch, you'd have 3 cables feeding into (and being monitored) by the Backup Gateway 2, one for each phase, and then you'd have 4 coming out of the Backup Gateway back into your switchboard and home circuits - three for the usual three phases, and another which powers the nominated "backup loads" at all times (ie. normally and during a blackout).