Arkaluu is not seeing anybody, no. He’s not really interested in any romantic relationships given his history of being used or abused for his position of power or money.
His last relationship ended when the woman he was close to just started flat out dating someone else without telling him, sending a letter - anything. His busy lifestyle had made the two of them that distant at the end.
He’s currently very close with his friend / fellow bookworm Zepsi, but both really are too busy and reluctant to enter a romantic relationship. He’s also fairly close with Faetrix, though that RP was time-shenanigan’d - but it should be canon in a few days when Arkaluu crosses into Draenor.