TLDR: you poll messages from RabbitMQ till the prefetch count is exceeded in which case you will block and only receive heart beat frames till the fetch messages are ACKed. So you can poll but you will only get new messages if the number of non-acked messages is less than the prefetch count. New messages are put on the QueueingConsumer and in theory you should never really have much more than the prefetch count in that QueueingConsumer internal queue.
Details:
Low level wise for (I'm probably going to get some of this wrong) RabbitMQ itself doesn't actually push messages. The client has to continuously read the connections for Frames based on the AMQP protocol. Its hard to classify this as push or pull but just know the client has to continuously read the connection and because the Java client is sadly BIO it is a blocking/polling operation. The blocking/polling is based on the AMQP heartbeat frames and regular frames and socket timeout configuration.
What happens in the Java RabbitMQ client is that there is thread for each channel (or maybe its connection) and that thread loops gathering frames from RabbitMQ which eventually become commands that are put in a blocking queue (I believe its like a SynchronousQueue aka handoff queue but Rabbit has its own special one).
The QueueingConsumer is a higher level API and will pull commands off of that handoff queue mentioned early because if commands are left on the handoff queue it will block the channel frame gathering loop. This is can be bad because timeout the connection. Also the QueueingConsumer allows work to be done on a separate thread instead of being in the same thread as the looping frame thread mentioned earlier.
Now if you look at most Consumer implementations you will probably notice that they are almost always unbounded blocking queues. I'm not entirely sure why the bounding of these queues can't be a multiplier of the prefetch but if they are less than the prefetch it will certainly cause problems with the connection timing out.
