As typically conceived, an economy based on endless growth cannot be sustained. Framing the question as "can a globally sustainable economic system maintain endless growth?" the answer appears to be that growth must eventually slow significantly but yes.

A recent study: Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies by Safa Motesharreia et al.

In sum, the results of our experiments, discussed in Section 6, indicate that either one of the two features apparent in historical societal collapses – over-exploitation of natural resources and strong economic stratification – can independently result in a complete collapse. Given economic stratification, collapse is very difficult to avoid and requires major policy changes, including major reductions in inequality and population growth rates. Even in the absence of economic stratification, collapse can still occur if depletion per capita is too high. However, collapse can be avoided and population can reach equilibrium if the per capita rate of depletion of nature is reduced to a sustainable level, and if resources are distributed in a reasonably equitable fashion. http://www.sciencedirect.com/science/article/pii/S0921800914000615

Faith in the collective power of the human intellect offers the hope that ways to increase the carrying capacity of the planet or extend the human domain beyond the Earth will be found. Who can say?