Can I plug a raspberry pi directly into the usb port of an offline computer, and automatically share them to a network folder over wifi?

Question

This may be a naive question, I've never tried this before.

I work in a lab where there are 20+ PCR machines each connected to a local, off-network PC hard drive & monitor which run software for the machine, and to collect & analyze data etc.

The problem is these computers/the software has totally locked out all internet functionality. Users are going up and down stairs through multiple airlocks repetitively all day to save the .txt data files onto a flash drive, carrying it upstairs to networked computers and moving them to a shared server. We frequently have failures of communication leading to different people collecting the same data multiple times and we generate hundreds of files a day. It is becoming ridiculous.

What I am hoping to achieve is to have a raspberry pi work virtually exactly like a flash drive does; plug 1 end of a USB cable into the device and the other into the computers usb port, have the software offer it as a location to save on like normal etc.

Then I want the raspberry pi to automatically upload any new data to a shared folder on the server over wifi and delete files from itself once they're on the network.

Is this a thing that could work as described? If so I would love some advice on what hardware to go for and/or any resources that might help. I've found a lot already but none of it describes exactly the thing I'm hoping to make. Thank you!