Just because rent seekers spend their money does not make them productive members of society. In nature parasites have their own parasites, which can again have their own parasites. I suppose in a zero sum economy rent seeking doesn't hurt the economy (just certain members of the economy), but in a positive sum economy, if non-productive rent seekers are taking money from productive people this will cause the economy to be worse than it could have been. If people who would otherwise be productive are lured into rent seeking by the potential profits then it's a double loss. Not only are they taking capital from productive people that could have been used to create more wealth, but they themselves could have been producing wealth instead of being a drag on wealth creation.
There are certainly situations where organizations that seem like rent seekers are not entirely rent seekers, though. Government is the main example. Taxes can seem like a drag on wealth creation, and sometimes they are, but they also fund infrastructure, education, and stability, which are wealth multipliers.
The issue is also complicated by the fact that the world economy is very connected, but economic growth is often measured on a per country, corporation, or even individual basis. Also, aggregate wealth is not the be-all end-all metric. Wealth redistribution can sometimes lead to greater aggregate happiness, even if the amount of wealth stays the same or even decreases.
Overall, though, I think that the majority of rent seeking hurts the economy and the people in the economy more than it helps, but I would be very interested to see empirical data showing otherwise.