Every polymer with an amorphous structure has its own unique Tg and also different variation of stiffness with temperature. Therefore, you should define which specific temperature you want to compare 2 polymers with different Tgs.
But let's assume that you want to compare the stiffness of two different polymer materials at room temperature (23 C). Should the one with lower Tg have lower elastic modulus than the one with higher Tg if we performed a simple tensile test at 23 C?
The answer is NO. See for example the following 2 thermoplastic polymers with very different Tgs that have however similar modulus when tested at 23C: