"an excessively congested link will see packets dropped when their time-to-live (TTL) expires."
I don't think that's true. When a packet passes a router the TTL is decreased by one, when the TTL reaches zero the packet is discarded. This is done primarily to prevent packets from ending up in an endless loop. Additional time spend in the buffer does not decrease the TTL any further as the TTL is not actually time related.
What happens with congestion is that the buffer of the router fills up because the packets cannot be forwarded fast enough, when the buffer is completely full new packets are discarded as there is no free memory to store them in.