MQ itself offers message-based communication between programs. You can't use it directly to transfer files. People talking about "sending files via MQ" often mean that they will write the programs themselves to read from a file, send over MQ, receive from MQ and write to another file. This sounds temptingly trivial at first but quickly becomes very complex if you want it to be robust. Not recommended.
What you should be doing if you want to involve MQ in your file transfers is use one of the file-transfer products that sit upon MQ. There are a number of mature offerings, about which I know next to nothing, together with a new product from IBM itself ("Websphere MQ File Transfer Edition") which is being actively developed and recently announced an updated version (7.0.1).
To answer your specific question, I've personally used WMQFTE to transfer a file of 1000GB from an AIX machine to a Windows one, so I don't think your "large" 100MB files will be a problem :-). I don't get involved with the mainframe as much but it is very much a core platform for FTE.