What you're asking to do is shady, even if you have the best of intentions.
Chrome developers have hardened Chrome against malware, and you see the results of that work.
1) Developer extension popup cannot be disabled. I quote the Chrome bug tracker on the feature request to make a setting: "Sorry, we know it is annoying, but you the malware writers..."
2) Silently installing an extension bypassing Chrome security mechanisms is blocked by securely signed preference files of Chrome. If you just add an extension where extensions normally are, it will not be enabled.
3) Actually interacting with Chrome to install an extension out-of-band is possible, but it's not going to be silent. Only for extensions in Chrome Web Store, you can modify the registry and let Chrome install it on next start-up. However, the user will receive a popup stating that an extension was installed by a third party, and offering to disable it. Once disabled, you cannot attempt it again (it will be locally blacklisted).
4) The only truly silent method is available to enterprise users. For computers that are part of a domain, the administrator of the domain can silently force-install extensions through domain policy. The user will not be able to disable the extension. However, this only works for domains.