USB interface to bluetooth interface for digital scale
No, an Arduino is a USB device and as such can only connect to a USB host or to a role-switching USB OTG device.  So it would not be able to directly connect to this scale device.

You can get a USB host shield for an Arduino, but it is quite expensive and very challenging to program.  You'd probably be better off with a compact embedded linux system such as a raspberry pi or beaglebone black, plus a bluetooth dongle (this will actually be cheaper than the arduino, host, and bluetooth shields).  However, if it's not known that this USB scale is usable with current desktop linux distributions, then you may find the project extremely challenging as you'll first have to research (/reverse engineer) the protocol used by the scale and implement your own driver.

Another possibility might be to use a compact embedded PC running windows as a gateway, if that is what the manufacturer provides USB drivers for.