Can I sync performances using the Arpeggiator with the BPM (clock) of an external MIDI device (master)?

Yes. You can select an external MIDI device (as a master) in [Sync Common] setting category < [Sync Source] of the GLOBAL menu.
For details, please refer to the [Sync Common] setting in the "GLOBAL settings" in the Operating Instructions.
You can download the Operating Instructions from the Pioneer DJ support page https://www.pioneerdj.com/en/support/documents/production/toraiz-squid/.