I am sure there is a hard limit but it may not be documented for the public but you will saturate the limits of your connection long before you hit it so it's a moot point.
Interesting question. The manual states the MSG queue length is dynamic. I'm sure we will never know as mentioned by The PLC Kid.
I would suggest that you program as many messages as you can be bothered copying, pasting and configuring and fire them all off once on the same scan cycle. The first four messages will go into the MSG buffer and will be serviced at the end of the program scan (or if called by comms service instruction). The remaining messages go into a MSG queue on a FIFO basis.
Quoted from 1766-rm001_-en-p.pdf Page 354
The buffer and queue mechanisms are completely automatic. Buffers are allocated and released as the need arises, and message queuing occurs if buffers are full.