Yeah that would work.

I just found this for stopping rugs slipping on carpet.

Double-Sided Tape

Step 1-Begin by measuring your rug with your tape measure; measure both the length and the width, and record these measurements on paper for reference.
Step 2- Measure 3 inches in from the perimeter of your rug, and apply strips of tape along the entire length of the width and the width.
Step 3-Once you have applied the tape, press the rug down against the floor so that it is firmly adhered.

Velcro tape

Step 1-Apply the scratchy side of the tape to your floor, sticky side down. This should, again, be measured at 3 inches in from where the edge of the rug will be.
Step 2- Apply the soft side of the Velcro on the rug, 3 inches in from the edge.
Step 3 -Position the rug over the tape on the floor so that the two sides of the Velcro are directly opposite each other. Press down on the rug so that the Velcro bonds.