To answer the last question first….Yes, there is the potential for a data transfer request to cause other requests to said file, to lock and therefore fail.
In terms of restricting the data transfer……
You can buy or write your own software to sit on the various exit points that control data transfers. (FTP, ODBC, etc). If you have money to spend, Vigilent from NetIQ is very good for this.
Alternatively, this might (and I stress the “might”….although, to be honest, I’m far from convinced that it will!!!) work for RUMBA (it certainly work for Client Access downloads)…..If you are running at V5R2 or higher, you can create an “Administration System” with Ops Nav and use the “Central Settings” to block use of file transfers (upload and/or download) on all 70 of your systems, in one easy stroke. You can even tailor the blocking to pre-defined users and groups.
This requires a fair bit of setup, and I would highly recommend you read the subject matter in InfoCentre, first.