Can DynaTrace monitor the fact that queues on middleware are filling up (if the agent resides on the application, not the middleware).
If you are referring to messaging queues, you might want to take a look at the MQ plugin. This runs on the ActiveGate so it is a remote plugin that does not need the agent to be running on the host to pull in MQ metrics.
Without monitoring the messaging queue depth (IBM MQ / Tibco EMS / ... ) the only method I can think of would be to define service-level metrics (EAP at this time) on the application side.
However, monitoring queue depths would be more precise by querying the underlying messaging technology for metrics.