Yes, this is possible and depends on a number of factors, notably stemming from the production (resin used, curing temperature, etc.).
Some recent data obtained (with thermosetting resins in wood particleboards, as example, with different particle size ranges) show that tests carried out in very different strain rates lead to statiscally different modulus of elasticity. The same has hapened in three point static bending tests..
Many polymer materials demonstrates rate sensitive deformative behavior when elastic modulus increases with strain rate growth. The same effect is observed in case of polymer based composites.
Dear Si Abdul, at high strain rate also we must take into account dissipative effects which causes the increasing of modulus of elasticity (in some cases, this effect is seemed very essential) . Corresponding value determines so-called dynamic modulus of elasticity. See, please, the paper on topic: Estimation of properties of elastomeric materials at constant rate of indentation // Journal of Friction and Wear. – 2001. – Vol. 22, № 5. – pp. 21–28. Good luck!