No! It does not have unlimited storage.
Google Pixel offers the user to backup their photos and Videos in the same resolution as captured to the Google Photos App. You can download this app on Android phones as well as on iPhones but you won’t get a same resolution backup, so you have to pay some amount, in order to get it to the phones other than Google Pixel.
Google is providing this feature in its phone as it's very common for an iPhone user to get “Storage is full” message. Google Pixel has a great camera, and thus, more will be the image size. In order to ensure that at least your photos will not eat much space, Google made it free for all Pixel users.
So, though it doesn't have unlimited storage, you can still be sure that your photos are at the right place at right time.
Does the Google Pixel really have unlimited storage? How?
No, it does not. But it does have unlimited Google Photos storage.
For device storage, you can either buy a 32 GB or 128 GB model. After Android software you and the basic Google apps, you should have 23 GB or 119 GB left, respectively.
For Google Drive cloud storage, you do not get anything extra. You are stuck with the original 15 GB.
For Google Photos storage, yes, you do have unlimited storage of any resolution photographs. The reason Google did this was to attract people to their product. They might be loosing 3 bucks a month in storage fees but they get a customer that paid $650+.