Per
@MathGeek attaching an external USB drive to the router's USB port is a "feature" offered by various routers.
However, attaching USB storage is very likely to slow network performance simply because the router is really not intended to be a "storage device."
The router's USB port only being very rarely used for ocassional purposes and/or "in a pinch" situations.
Likely no harm per se with trying the router and a USB connected drive.
May or may not be viable with respect to the router, disk drive, and hosted network.
Just be ready to undo if necessary.
Check the router's User Guide/Manual for instructions and details.
And, as always, have all data backed up somewhere else as well.