Yes, of course it could. Whether they do is another matter as even Uber will not be running all their business off a single server - they'll have web servers to receive requests, application servers to process the data, and a (clustered?) database server to store the data. (well, I assume they do, chances are they are running it all off a single websever running PHP for all I know).
Servers are very powerful nowadays, for £20,000 you can have a 32-quad-core-cpu with gigabytes of RAM and several network cards. The server processing game changed about ten years ago and made practically unlimited computing available, hence the rise in cloud services as providers had more power than they knew what to do with!
I do know that I used to work for a financial services company that had a trio of servers that was rated for 400,000 transactions per hour. The solitary performance test server could handle way more than 2 requests per second, and this was quite complicated transactions involving a lot of data transfer, aggregation and checking. I also worked for a company making emergency service control systems, thousands of vehicles sending in location data isn't as heavy a load as you'd think, its very easy to handle large amounts of data packets like this, storing them was more of an issue (and you simply cache them in RAM until you have a block to persist together - assuming Uber has the same audit requirements, they could just be keeping the last-known location and throwing away the rest)