Let's go theoretical for a brief moment. CDO is a very simple but very effective facility for Access (or in fact, any other VBA-using utility) to send mail. The question was asked about whether CDO works with GMail or other outside clients. The answer is "No, it does not need to."
Outgoing mail is, for most of the internet, sent via a protocol called SMTP - whether we are talking CDO or Outlook or something else. Though it has extensions for binary attachments, SMTP or "Simple Mail Transfer Protocol" is actually just a literal text protocol. It does not need to have a local client like Outlook or Thunderbird or whatever other local mail clients might be out there. Instead, when you use CDO, you supply the destination address in a "username@web-path" format - where the web path is a computer name and the other part is the targeted recipient of the mail. And that "other part" has to be the name of the person on the destination system. So what happens with CDO?
Like any machine on a network that has some kind of ISP router or domain controller (either one, or both), there is an address defined on your machine as your "SMTP Gateway." What happens is you don't send your mail to the "web-path" in your destination address. Instead, you send your mail to the gateway and the gateway device will do the rest. All that CDO has to do is open a network link (socket) to the gateway and say "HELO" to port 23 of the gateway machine. Then it starts the protocol with "SEND" (yes, literally those letters in that order). When the gateway responds, CDO sends "TO username@web-path" - and there are other parts of the protocol for attachments, subject line, CC and BCC, and stuff like that. CDO formats the text it has to send to the gateway, then using the link it just opened (to the gateway), it crams the mail message down that pipeline.
When the mail message is still initially being received at the gateway, that system looks up the "TO:" address and determines a proper route. If a route is determined by the gateway, it pushes the message along. OR if there is a problem, an error is returned in reply to the TO: part of the transmission. So all that CDO has to do is test for a success or failure code on the reply from the gateway. You get a success? Keep on sending. You get a failure? Report it to the user and clean up the mess.
If you have ever heard the term "Store and Forward" in the context of the Internet, this is a PERFECT example of a Store and Forward protocol. And because it is so simple, CDO can do those steps without the help of a mail utility.
Note that RECEIVING a message is a bit more complex and uses a totally different protocol. You usually need a mail client for this function. CDO does not include the required reception protocols. This is why you can use CDO to send mail but not to receive it.