Relay Data through pins (USB)

Hello!
So I am working on a project (or will start to work on one) that will include relaying data from one win to another.
What I mean by this is for example you have a USB thumbdrive, you want it to be connected to pins 3,4 (along with the VCC and VDD), then you have another USB connection, this time leading to pins 5,6.

What I want to happens is when you plug the USB cable (the one attached to 5,6), your computer recognizes the thumbdrive.

Is this physically possible?
Thanks!

Is this physically possible

No.
You are thinking that you can just connect two pins of an arduino to a USB memory stick then you can't without a lot of trouble. Connecting two such devices will just exceed the memory and speed capacity of the processor.
Even the direct connection of one USB device is a major undertaking without extra hardware like:-
http://www.parallax.com/Store/Microcontrollers/BASICStampModules/tabid/134/List/1/ProductID/434/Default.aspx?txtSearch=usb+datalogger&SortField=ProductName%2CProductName