No, due to the very nature of the elastic itself. Every time the elastic expands, it will break the adhesive bond and the Velcro will pop off. You can always use the sew-on type of Velcro on elastic armbands, though!
Velcro Patches have not commented on their next venture in the arm bands, but it is very unlikely that they may stick in one product design. Companies usually look for ways to to satisfy their customers and will try out various ventures to make this happen.