[SalesForce] Override background image/color in the community using the Napili template

If you upload you image to a static resource. Yes.

All you need to do is go under the "Branding editor" -> Edit custom CSS and add the appropriate styling. Reference your image accordingly:

body
{

    background-image: url('https://salesforceDomain/resource/"generatedID"/StaticResourceFile/img.jpg');
    background-repeat: no-repeat;
    background-size: cover;
    background-attachment: fixed;
}

salesforceDomain -> I am assuming you know what this is...

"generatedID" -> Salesforce bundles your static resource folder into some generated ID. In order to obtain it, you can reference the image in a visualforce page and load it. Using chrome's developer tools, under the network tab you should be able to view the Request URL for the image.

VF page:

<apex:image url="{!URLFOR($Resource.FolderName,
                  'filepath/ImgName.jpg')}" />

Chrome dev tools:

as of winter 17, you can create a Custom Theme Layouts which basically involves creating a lightning component, referenced here.

there is a more recent post in the forum that also mentions custom layouts in the Napili template here.

You can create a Custom Theme Layout which basically involves creating a lightning component, referenced here

and add the New Theme Layout through the community Settings:

You will then want to create a Page Variation which you can assign to different profiles referenced here Page variations allow you to specify what profiles access what page. From the community builder, select the page you want to create a variation and select the cogwheel (settings) that appears next to it: from there, you want to create the page variation and save it. This will allow you to select the audience criteria under the page settings:

and select the profile that should be directed to the page variation:

Now, Once you created your Custom Layout (so pages are different from one to another based on profile) you want to go to each of your page variations and select page properties under each: and assign a Theme layout to each page variation (make sure the correct page variation is selected when you do this)

Repeat for each page that requires a variation and a different layout.