I like to overanalyze things, so let's have a go!
What's a desktop anyway?
Is there a significant difference between a docked laptop and a desktop, except you're able to undock the laptop?
I think the key descriptors to a desktop are:
Physically separate human-computer-interface (HCI) from computing device.
Computing device is in physical proximity to the HCI.
Given those constraints, I could imagine the desktop being replaced in many instances by thin clients, particularly in the corporate world. A virtualized remote desktop is cheaper to maintain, easier to scale, and with gigE+ networking capable of low latency interaction and high computing power.
Currently the prohibitive factor to wider adoption is the associated licensing cost and hardware cost, as many solutions require proprietary everything.
The docked laptop from my initial question clearly is a desktop, when used with screen and mouse, which is usually the case in a productive setting. My corporate experience has been that laptops are often issued to everyone, as some mobility is expected, but due to the technical constraints of the platform, I had to get an additional desktop and access to additional compute hosts at my last job. This makes the laptop-by-default policy not very cost effective.
And finally, by going back to a more literal interpretation of desktop computer: As long as people will work with computers, they will do so at a desk. The computer on that desk, will be their laptop computer.
Regarding the issue with the mouse:
By reducing the scope of the word mouse to a physical pointing device that glides over a flat surface and offers buttons for interaction, they may not be around forever. From my experience with mice, getting them to be decently ergonomic is a tough fight.
Many alternative pointing devices exist, from trackballs, to trackIR to touchpads, touch screens and relative pointing devices such as the touchpoints on some laptops. Pens, 3D-mice, gesture control, eye tracking and even pedals or other foot-operated interactions may well prove to have a future. I once used a scroll bar for two weeks, which doubled as a mouse, to relieve some shoulder strain - I didn't keep it because it induced finger strain....
On the other hand, the mouse is currently being borne on some massive momentum. Everybody that is using a desktop computer is usually learning to do so with a mouse. While touch screens may be creating a new generation of users, they're less useful in larger devices, unless the point of the interaction is to demonstrate that the action is being done - think collaborative work (a classic collaborative workspace is an airplane cockpit, where each pilot needs to be aware of the others actions to be able to accurately judge the situation of the airplane), teaching, etc.
Another current, and momentum-relevant advantage of mice is the cost-effectiveness. Ever since optical tracking has been perfected, there's no more cost effective means of precisely pointing. All the alternative devices I listed either carry a higher price-point with no true gain in accuracy, or suffer significantly lower accuracy at a lower price point.
Finally, consider that with ever larger screens with more pixels, pointing becomes more and more a multi-scale problem. A pointer-accelerated mouse is well suited to this challenge.
This concludes my overanalysis. TL;DR: No.