You have found a fixed, non-zero acceleration. Surely you can see that this shows the helicopter accelerating forever?
Without air resistance there is nothing to oppose the acceleration of the body, and as such there is no terminal velocity.
Also, bear in mind that although air resistance will be minimal it will always be proportional to the square of the velocity, as the body of the helicopter will be immersed in a turbulent flow.
To solve the problem you want, you need to solve the following equations:
...where alpha is the drag coefficient for the helicopter (look it up for a model helicopter), and Fx and Fy are the x- and y- components of the thrust force. You have solved for Fy, so you can just input Fx from the tangent of the tilt angle.
At terminal velocity you will have du/dt=0, so:
u_terminal = sqrt(Fx/alpha)
