Negatory. You don't loose DOF at the ACTUAL focal length. You'll loose DOF at the GIVEN Field of View (which I find it to be just confusing marketing terminology)
To make things Easier, just think what a crop sensor is:
Cropped. Your image that you take, but cropped. Your bokeh Remains EXACTLY the same as you would see in a full frame 35mm, but just less coverage.
Sure you can convert all you want, and give it equivalent values, but one thing is 100% certain: you just have a high MP "Tighter-cropped" image.
Canon backs this with their sensor comparison chart. There's no zoom, (unless you count it as "digital zoom") as optically, you're seeing the SAME image, just smaller, but higher MP to blow up to a bigger size. That's where Pixel Density comes to play.
SP12 is right on the nose. You're thinking in terms of Field of View. Which EXACTLY means: Because it's cropped, it "should be a longer focal length, and the bokeh SHOULD increase dramatically because of the longer focal length but it doesn't so we'll have to increase the f-number".
Remember 3 things affect DOF: Aperture, Focal Length, and focus point (Distance between subject and the camera)