Nope.You climb up the Burj Khalifa and you can still see a horizon. Same at 35000 ft, it's still away over there somewhere. Now look at the horizon from your pilots seat through the airplane window and maintain that same altitude (I know Geoff), and you are going to be flying parallel to the ground because the horizon is not a fixed point on a round earth. So round and round you go until you run out of fuel.
But it is of course a fixed point on a flat earth (the edge) so you'll hit it eventually.
If you look at my earlier image, on a round earth if you fly directly towards the horizon you will follow the dashed line up to the point of the "splat". Because you are getting lower and lower the distance to the horizon gets shorter and shorter until you hit the ground.
Your point is premised on maintaining the same altitude and not at flying directly towards the horizon. And if you maintain the same altitude you don't crash in either case whereas if you fly directly towards the horizon you crash in both cases.