Here is how you can promote events through a MailChimp email list and get people to register or RSVP, while driving more traffic to your website in the process. MailChimp support arrived in RSVPMaker with version 4.0 and makes it easier to craft broadcast email messages that incorporate RSVPMaker events and other WordPress content.
You begin by composing the content of your event using the standard WordPress editor. I will use the example of a July 20th webinar I’m planning.

Below the content editing area, you will complete a series of event options such as the date and time. Here, I’m asking for people to register so I’ve checked the Collect RSVPs checkbox.

Because this event is a webinar, I’ve created a detailed confirmation message that includes the links people will need to follow to attend. You can see a little of it on the screen above, but I composed it by clicking on the Hangouts Setup link and following the prompts to set up an HTML message like the one shown below. (See more about support for Google Hangouts on Air).
I’ve also set the website to send a reminder message to attendees two hours before the event.

I also customized the signup form, mostly to simplify it by eliminating options like the blanks for adding guests (which make more sense in the context of an offline event).
I also specified that I would like an “Add me to your email list” checkbox to appear on the signup form. This will allow people who aren’t already on my email list to join it at the same time that they complete the RSVP form.
In other words, I hope to build my email list at the same time that I am registering people for the event.

Once I am happy with the event I have created, I can create a draft of a broadcast email message based on that event.
A Send Invitation link now appears on the listing of events. There is also a Content for Email screen you can use to select content to be included in an email broadcast (which also allows you to import blog posts or listings of posts).

Imported content is loaded into the WordPress editor, now being used to compose email content. The default title includes the title of the event, along with the date. The email message does not necessarily have to include the verbatim content of your event, but you can use this as a starting point for your invitation email. The imported event includes the RSVP Now! button to encourage people to respond.
Imported content also includes a placeholder (the “INTRO” text) for you to add an introductory message.

Once you are happy with the content of your email broadcast, you can preview it on your website. It will be displayed in a special template specific to events. You can customize the HTML to be used in the template from within WordPress to add elements such as a logo or change the default background color.
If you see changes you want to make, click Revise to go back to the editor. I also typically send a preview version of the email to myself before submitting it to MailChimp.
When you are ready to send your broadcast, check the MailChimp list checkbox, confirm that you have the right list selected, and click Send Now.

I’ve actually used related techniques to send email broadcasts and regularly scheduled event roundup newsletters to various communities for several years. That approach has also been standardized as part of this latest RSVPMaker release.
As you can see, I’m planning a July 20 webinar to showcase these features and gather feedback on how to make them better. Try it, and let me know what you think.