Probably a no. A normal LED is designe to spread the light in a certain way. Same is for the LED in the mouse.
I'm far from an expert on LED so this is kind of speculative from my side. I'd expect that a LED for a mouse have a more narrower spectrum band since we want to avoid noise, and also I'll expect it being designed to spread the light in a certain way - again in order to avoid noise.
When that said, It is an interesting idea - to try see if a mouse will indeed work with a "regular" led as a replacement.