No. There are several issues.
First, a minor issue is that a lot of the code they use is PHP - PHP doesn't work great for desktop applications - a desktop application would have to be completely re-written in some other language.
Second, You would have to buy NetfabbPro and add the Shapeways customizations to it, turning it into MeshMedic. Shapeways does not have the rights to distribute NetfabbPro to you, so it would be a separate cost and separate installation. NetfabbPro is quite expensive for commercial use.
Then, you'd have to have direct interaction with the databases and the whole CloudFlare structure, aka the message "It will take some time for your changes to propagate". That is not going to happen. That part must stay under control of code that Shapeways maintains.
Another good bit of time is spent on the 3dTools checks. My personal opinion is that this is one area where Shapeways could significantly improve processing time - allow a shopowner to set a "default" material in their shop, and process that material first, rather than the sequence of all 41 materials they currently use.
Lastly, even if they did create a desktop application, there is the issue that materials are constantly being added, and the material guidelines are tweaked quite often. There would have to be some way to keep your desktop installation constantly updated with the most recent materials and rules. You could create a situation where you checked the rules with an older version that is no longer applicable, and the rules would have to be re-checked on upload anyway.. causing a doubling of the time it takes to upload.