How would you propose doing this? AFAIK you would need a driver to handle the mirroring (I'm not aware of one that will mirror to a USB device), and it would very much depend on how that driver works.
Assuming that such a driver exists and it was well-designed for that kind of scenario, I'd expect that if the system experienced persistent heavy disk I/O write load scenarios that at some point the driver would have to slow things down a bit in order for the USB device to catch up. The WD Black in my system peaks at about 180MB/sec but a modern SATA drive will also be able to do NCQ. A USB 3.0 device would AFAIK be held back by the extra overhead in talking to USB as well as the lack of NCQ.
Of course I've been assuming USB 3.0 rather than 2.0 the whole time.
Having said all of this, I can't think of a single good reason to do this. A decent backup system would be better than mirroring IMO, and performance would likely suuuuuuuck if the internal drive failed. In order to make the whole exercise worthwhile you would need to the be sure that the driver software allows you to re-image a new internal drive from the USB. More than half the point of RAID1 is the minimisation of downtime, and the difference between super-sucky performance and downtime is not as black-and-white in reality as it might appear.
IMO If you need mirroring as well then use a SATA drive internally.