Is this non bank branch/company part of your organization or a totally separate entity?
I can't think of a good reason not to allow other than the normal security issues you have with any RDC customer. You might have concerns over how many employees will have capture access, control of physicl checks after capture to prevent them from being double captured, etc.
However, if I am the non bank and I am NOT part of your organization, I'm probably going to tell you that I'm not doing anything other than putting the deposit together and letting you pick it up, unless you want to pay me more money to do this function. In the end, it might not be cheaper.