So let me rephrase the question slightly...

Is it possible to link a device, created by copy/paste with the context menu in the Model Designer window of CCP, to a device LCD button, in the same way that devices created using the 'Program/Create & Name Devices' menu are linked to their device LCD buttons?

A second question, which perhaps renders this first question moot, does it even matter?

I've been playing around with devices created both ways, and I am not finding any obvious difference other than their behaviour when being deleted.  I just want to avoid any problems down the road that might be caused by my overlooking something here.

Thanks.