Garrett Wang, the actor that played Harry Kim, has recently confirmed that he has no idea why the Borg Queen said that she'd see him soon.
@elroja65 : Garrett do you know what the borg queen meant when she
said "We'll see you soon, Harry" in Unimatrix?
@GarrettRWang : Other than that being super creepy? no, I have no idea
what the Borg Queen was referring to lol
In the absence of a canon confirmation, I can offer some possible alternatives;
- It was a plotline that never got followed through.
- It was a threat against Janeway (e.g. knowing how protective of him she was)
- It was a threat against the crew in general
- It was intended to shake him up personally
I veer toward the second option. Janeway is attacking the Borg on a very personal level and despite her somewhat cold demeanour, it's clear that the Borg Queen views the whole unimatrix fiasco as an attempt to damage the collective and lessen their perfection.
She's saying, "If you come at me and mine, I'll come at you and yours".