Yes, the Samaritans are Israelites.
Samaria, the Samaritan kingdom, is in this context the Kingdom of Israel, i.e. the northern part of the Biblical United Kingdom of David and Solomon. The Samaritans, and other Jewish groups living in the Kingdom of Israel are listed as Israelites and descendants of Abraham in the Bible.
However, here is the Judean account from the Book of Kings of the the Assyrian rule over Samaria:
In the ninth year of Hoshea, the king of Assyria took Samaria, and carried Israel away unto Assyria, and placed them in Halah, and in Habor, on the river of Gozan, and in the cities of the Medes.
And the king of Assyria brought men from Babylon, and from Cuthah, and from Avva, and from Hamath and Sepharvaim, and placed them in the cities of Samaria instead of the children of Israel; and they possessed Samaria, and dwelt in the cities thereof.
In other words, it is claimed that during the Assyrian period, all of the people of the Kingdom of Israel were replaced with people not descended from Abraham, and that the Samaritans later acquired the Jewish religion from the Kingdom of Judah.
The account of the Assyrian King Sargon in the Nimrud prism at first glance seems to agree:
I repopulated Samerina more than before. I brought into it people from countries conquered by my hands. I appointed my eunuch as governor over them. And I counted them as Assyrians.
However the prism also says that 27,290 persons were deported, and numbers in texts such as the prism, written to extol the power and might of a king, tend to be inflated. Still, 27,290 represents only a small fraction of the apparent population of The Kingdom of Israel at that time.
As such, the Nimrud prism does not support the claim that the people were replaced by foreigners. Instead it's likely that only the aristocracy was deported and replaced by people from other lands, in a "divide and conquer" style replacement.
This is typical of all ancient claims of one people coming in and replacing another, from the Exodus, to the claims of Anglo-Saxons invading England. Neither genetics not archeology tends to support these claims. There are seldom any cultural changes in the archeology, and the genetic influences are generally only in a small percentage of the population. This is true also for the Assyrian invasion, where there is continuity in occupation of the sites before and after the Assyrian invasion. [ref]
So there is truth in both accounts: People were deported, and other people brought in. But the claim that all of the people were replaced by foreigners is supported neither by the Assyrian accounts nor the archeology. Undoubtedly the vast majority of the people living in The Kingdom of Israel before the Assyrians arrived remained there, and the Samaritans therefore have as a good a claim to be Israelites as mainstream Jews do. This is also supported by genetic studies indicating that the Samaritans have a closer paternal genetic relationship to other Jews, than to non-Jewish middle eastern peoples..
However, when it comes to the question of whether the Samaritans are in fact descendants from one of the twelve tribes of Israel, this claim is much harder to verify, for the simple reason that we can't verify the existence of these twelve tribes.
It is claimed that Israel and Judah was made up of twelve tribes and that these tribes were united into one kingdom sometime before 1000BC, a kingdom that then was split up into Israel and Judah after the death of Solomon. But there is no way to verify this. The texts that claim this are written many hundreds of years after the claimed events took place, and there is no cultural difference between these tribes that is detectable in archeology. Hence, discussing if the Samaritans are descended from one of these tribes makes little sense.