Hello there!
Theoretically it would be possible but it would not benefit you in any way. The thing is laptops are thin... very thin... with very limited space compared to pc-s..
Which basically means that they needed to build laptop cpus in a fashion that produces much less heat and the cooling largely depends on the controlled and designed airflow provided by the case itself. On desktops however they can go wild since they have plenty of space.
Thing is.. even with a dead fan your desktop coolers heat-sink probably provides far better cooling than any laptop cooler would.
What you can try is to take the fan only and mount it somehow on the heat-sink in your desktop... but that would also be silly, since the laptop fan is really small and wouldn't really change anything... You would be far better with the cheapest desktop cooler on market.. or just mounting a simple case-fan on your heat-sink.
Hope that helps,
Cheers!