How to extend detection distance of computer mouse?
Yes, what you suggest is possible. (Congratulations on your cogent thought process).

The mouse navigation compares "features" from one image frame to the next, and calculates how much X-movement and Y-movement has transpired. If no image features can be found, then no movement can be calculated. An out-of-focus image contains no features: a mouse's lens is extremely near-sighted.

A lens of a different focal length can focus further away. For example, a fixed focal-length camera usually extends focus to infinity. Doing this converts a mouse to a camera (See my profile photo; it was done with this modified mouse):


Having a sharp focus very far away likely allows features to be found, and XY movements to be calculated. Still, pointing it at a featureless sky would confuse the internal calculator, and yield no motion-detection.
However, the mouse is now useless as a mouse on a mouse-pad because features very close are out-of-focus.



Notice that the mouse's LED light source has been removed. Daylight is sufficient to create an image. The internal chip can accommodate a fairly wide range of light levels (but not as wide as your eye).
For a mouse on a pad, the LED is needed for illumination, since the mouse itself shields room light from the small space between mouse and pad.



The plastic lens included with this mouse could not be moved close enough to the internal chip to allow infinity-focus. It was replaced with a 4.5mm focal length plano-convex glass lens. The lens quality need not be high since pixel-count is so small.
 Lens is mounted in a machined-brass housing that press-fit over the ADNS-2610 chip's cover. The tiny cover hole (to allow light inside) was drilled out to about 3mm dia. The cover has a 5.6mm diameter step over which the brass housing press-fit. The cover can be pried off the chip with care.
Interface to this 8-pin chip is serial I2C. This is an older chip that requires +5V Vdd.  Avago data sheet is very well-done.

Have tested its XY scanning ability with infinity focus, but not used it as a mouse this way: you may find that much gesture movement yields small cursor motion on your screen.
More modern chips provide more pixels and pixel download rates are fast enough to allow video frame rates when used as a camera. Getting data sheets for them and getting small quantities for experimenting seems to be a problem.