Forwarding text messages from an android phone to a TCP port of a PC
It isn't difficult to create the necessary code to listen to incoming messages, handle their data and send them to a TCP socket. I've done such an app but can't release it's code, unfortunately. All I can say is it's pretty simple, just research incoming SMS handling (for example here) and sockets (for example here).

As to your other question, there is some latency when receiving SMS, but this depends on your carrier. They store the messages in a queue and send them to your phone as fast as they can. So, depending on your carrier they may have some limits on how many messages they accept into the queue.

You can estimate the delay in the messages by sending a SMS to your phone from 2 other phones simultaneously, and check the difference in receiving the messages. You can then estimate the handling speed per minute. For example, if there's a two second delay, it would take (200*2)/60=6m40s to process 200 messages.