By importing external images I mean making and keeping local copies of all the linked images in posts and pages, adding them as WordPress gallery attachments of your WordPress site.
By using Import External Images, a WordPress Plugin you can do this so that in future in case if the image owner site if removed any image which you are using then in that case you will be having a local copy of that image.
Actually this plugin examines HTML source of your blog post at the time you save it, inspecting each IMG tag, and processing them according to the options you have selected.
Under the default settings, it finds IMG tags having links to images on external sites and then it copies those images to your WordPress site, updating the IMG src to point to your copy and yes it works in multisite too.
In case if you don’t want import images from any third party image hosting site then you may make this plugin ignore particular domain name you want from the settings page.