In practice you should not have to do anything other than perform a normal copy. E.g. if the object has a reactor attached to it, that same data will be copied to the new object. Thus the new object will also fire the reactor if you subsequently change it.
I'm not sure of anything embeddable in a DWG concerning reactors. The only embeddable stuff would be VBA code, and then you usually get confronted by an "Enable Macro" dialog whenever you open the DWG. I've seen some attempt at embedding LSP as XData / XRecords, then using an embedded VBA to load that LSP whenever the DWG is opened.
The problem with this approach is the client needs the VBA interpreter installed, which is not standard with the newer ACads.
Personally I'd create an installer for the LSP - have it load for each DWG through the acaddoc.lsp file (or whatever you prefer). That way you can send your installer to each PC which will work on these. ... Actually on second thought, I'd then also try to avoid persistent reactors.