No. Carriers will not be severely affected by the LTE iPhone when it runs on its own LTE network.
LTE is considered a
big improvement over 3G, where network capabilities and capacities are much higher and larger than what 3G can do.
The reason why carriers are moving customers towards 4G LTE is because LTE is simply capable of handling much more customers than what 3G does. LTE has up to 4 times more bandwidth and capacity than 3G, not to mention enormous speed improvements.
Hence, to reduce the 3G network's load, carriers are moving customers to LTE. This shows that carriers have absolutely not much of a problem with more and more customers on 4G. 4G, in fact, is a technology that should have realistically came much later, maybe starting next year assuming there is breakeven usage. However, due to more and more customers demanding for data services, 4G is quickly pushed around the world, such that even carriers are actually calling 3G HSPA+ networks 4G
In the worst scenarios, we can expect some slowdown in data speeds. But data speeds will always be much faster than what you get from 3G