Yes, as explained in this blog post Stack Exchange is a Imgur customer:
Alan Schaaf, the man behind Imgur, generously provided us a network-wide “pro” account that keeps any images hosted through our websites around indefinitely.
They have their own sub domain on Imgur (i.stack.imgur.com
), where images never expire for example. Profile pictures are uploaded automatically to Imgur if you set one from your profile. They use the Imgur API to upload images.
It is possible that profile pictures are coming from other sources though. For example when you log in with your Facebook ID, it will load the images directly from the Facebook CDN.
You can use the Stack Exchange Imgur account to upload images from the upload dialog when editing posts. That is the only way to upload images there.