Optimal scalability of a distributed algorithm
Yes, your intuition is correct, for all the reasonable models of computation that I'm familiar with.  If it weren't, then we could take a single machine and have it simulate a cluster of n nodes, increasing the cost by only a factor of n.  So, if you had an algorithm that ran on a cluster of n nodes faster than T/n, you'd get an algorithm that runs on a single node faster than T.

Note that the single node might need to have n times as much memory as each node in the cluster.