Your character is born on a certain day to uncertain parents. So far, so prophecy. Then you are inducted into the Blades and sent on the main quest by them. Does this mean that the Nerevarine is a pawn of the Empire?

I think 'pawn' may be inaccurate for the player, but better for Caius, The Blades, and the Emperor. I always felt the Moth knew exactly what they were doing and felt you far too valuable to sacrifice on a political gambit against primitive Ashlanders. Anyways, I'm in no way a lore expert. I would suggest that you ask a moderator to move this to the lore forum. Them guys down there eat this stuff for lunch.

Moved accordingly.

The Empire only thinks the Nerevarine is their catspaw.

Azura called all the shots, possibly up to and including finagling an Elder Scroll and convincing the Emperor that this prisoner was actually a suitable candidate to fulfill the prophecy.

Some of the lore forumites, myself included, interpret "Morrowind" as showing the Nerevarine is a puppet throughout; to the Empire, to Azura, to Helseth at one point, to Almalexia, and to Vivec. To me, the Nerevarine after the main quest's end is finally pulling his or her own strings. I wouldn't be surprised if he/she travelled to Akavir out of curiosity, as an amateur explorer.

Though the Nerevarine was ultimately a puppet who destroyed the Tribunal and laid the groundwork for the Red Year destroying Morrowind, hurling the surviving Dunmer into a diaspora, it was all probably fated, and necessary. If it weren't for the player character, Dagoth Ur would have ruined Tamriel and eventually the other continents, leaving only slaves and Lovecraftian monsters. Also, this is not the end for the Dunmer -- it is the beginning of something. Probably an evolution, while they're in diaspora, away from their clannishness and insularity. They're now forced to be citizens of the world, though it's unfortunate that they've lost much of their roots.

The Nevarine is a pawn of the Emporer, who is acting as a pawn of Azura, who has been duped by Mehrunes dAGON. Only because the Heart of Lorkhan was removed could Dagon pierce the Liminal barriers even with the deactivation of White Gold.

Your fate is your own in Morrowind..the last boss of the game even lets you choose whether you serve the Empire or are a self styled hero.

Or is in fact, Nerevar Reborn, by the will of the gods and fate.

Yeah..there was even a fourth "I don't know" option I believe.

Ur seemed to respect each of these decisions except for the "Serve the Empire" one. He welcomed Nerevar and he admires self styled Heroes as he fancies himself one.