Yes, but with story-continuity caveats
The lore regarding Tiamat is varied, it has been interpreted and reinterpreted many times throughout the editions and campaign settings. In 4e and 5e, Tiamat and Takhisis have been confirmed to be the same entity, so the lore also includes many Dragonlance stories. Here are two actual examples of Tiamat/Takhisis being killed on her home plane:
- In the Dragonlance Legends trilogy, we have Raistlin travelling to the Abyss (the outer plane where Takhisis is said to reside) and is able to kill her. She is gone for good (though further events revert this outcome).
- In the Last Breath of the Dragon Queen (Dungeon magazine #175, 4e, Nentir Vale campaign setting), which is the last adventure of the Scales of War adventure path, the adventurers travel to Tytherion, a plane in the World Axis cosmology that was home to Tiamat. If they manage to defeat Tiamat, she is gone for good.
So in principle, at least as far as particular campaign worlds are concerned, the lore has examples of Tiamat dying in her realm and staying dead.
Then the next question is whether Tiamat's home realm is in the Nine Hells or not. Regarding this, here are some pieces of relevant lore:
- As you have mentioned, Tiamat is explicitly mentioned in the article Rearranging and Redefining the Mighty Dragon (Dragon magazine #38, June 1980, page 41) to be a devil and reside in Hell (alignment LE).
- In Dragon magazine #75 (July 1983), in the very first fleshing out of the Nine Hells in D&D history, Ed Greenwood specifically assigns Tiamat as the ruler of Avernus, first layer of the Nine Hells. This is such a classic article that it was re-printed in Dragon issue #400 (June 2011).
- The 2e Planescape sourcebook On Hallowed Ground demotes Tiamat to "a watchdog position at the entrance of Dis" from being a Lord of the Nine, but her lair is still on Avernus.
- The 3e Manual of Planes places Tiamat again on Avernus, guarding the access between Avernus and Dis.
- In 5e, she is the main villain in the very first adventure story-line, where the heroes are trying to stop the Cult of the Dragon's attempts to bring her from the Nine Hells to Toril. (Furthermore, according to the 'next' adventure Storm King's Thunder, when the heroes officially became successful, and Tiamat was banished to the Nine Hells.)
Hence, she has been a resident of the Nine Hells in almost all of D&D history, and counts as a (arch)devil in some of the editions. Besides, as we discussed earlier, deities can also be slain in their home planes.
There is only one complication: Tiamat is a multi-spheric power, she has worshippers in many crystal spheres, so being killed, even in her "home plane" might not mean the end of her completely throughout the multiverse. Examples of this situation are described in 2e Forgotten Realms sourcebook, Faiths and Avatars:
Incidents that occur on one crystal sphere are not relevant to the dealings of that deity on another. Only incidents that affect a deity on its home plane of existence (usually in the Outer Planes) affect the power in all crystal spheres, and even then one has to be careful not to assume too much. So, beings who are multispheric who die in the Realms have merely involuntarily or voluntarily severed their divine connection to Realmspace. They are not dead, but they might as well be as far as the inhabitants of the Realms are concerned.
Perhaps an example would serve to illustrate this. In a far-off crystal sphere a power of evil who manifests herself as a multiheaded chromatic dragon has recently been rumored to have died. She was known to the natives of the sphere as Takhisis. A group of powerful adventurers from the Bloodstone Lands in the Realms met and killed a powerful multiheaded, chromatic dragonlike creature on one of the lower planes some years ago. It was known as Tiamat. It may have been a manifestation of a deity, or it may just have been an extremely powerful planar being. In the land of Unther, also in the Realms, until very recently the majority of the populace belonged to the Cult of Tiamat. Tiamat’s avatar died during the Time of Troubles at the hands of Gilgeam, god-king of Unther, who himself died recently.
The being called Takhisis on one crystal sphere may or may not be Tiamat, and in any case her rumored demise had no effect on events in the Realms. From this we can assume that either Takhisis is Tiamat, has a presence on multiple crystal spheres, and is thus not dead—or she is dead and is thus not the Tiamat known in the Realms.