Can arduino create a file in its memory?
To answer the original question: Basically, yes, you can write libraries to implement a file system using the memories of an embedded microcontroller. 
However, if it's feasible highly depends on the controller architecture and its peripherals. 
Some of them (e.g. the one on Arduino Due) allow Flash reprogramming while an application is running from Flash.
Others require to have the application running in a special boot block or even in RAM when accessing the Flash for writing (this should be the case on an Arduino Uno)
And others don't allow Flash accesses from application at all.

Anyway:
The use of this for your purpose is very little, because the interface to the PC would also have to support the file system (for example, you could implement a FTP server and use an Ethernet connection...). 
Therefore, the SD card approach is surely a very good suggestion.