Yes, but not on Attic black-figure vases. However, one of the most famous Greek vases -- alas now lost -- is a 'Chalcidian' amphora from around 540 BCE showing Aias and Glaukos fighting over the fallen body of Achilleus (complete with arrow in his ankle ... and his back too). Well, I say 'famous': maybe it wouldn't be so famous if not for its cameo appearance in the film The Incredibles (2004) as part of the decor of Edna Mode's house. Here's an image from before it was lost, reprinted in Steven Lowenstam's 2008 book As witnessed by images: the Trojan War tradition in Greek and Etruscan art.

In Attic vases, his death isn't shown: you may be aware of a tendency in Attic art to avoid moments of direct action, in favour of the moments leading up to the event, creating a sense of anticipation; or directly afterwards, showing the aftermath. But there are vases showing his body being carried off the battlefield by Aias -- there's one such image on the François vase; and plenty of vases use a similar composition, showing one warrior carrying the body of another warrior. Here's an example dating to around 510 BCE.

But I must caution you against treating Greek vases as illustrations of texts. This was a habitual practice among scholars up until the late 1900s. And it's absolutely wrong. For one thing, epic wasn't a particularly prestigious genre of poetry until the late 500s BCE. For another, artistic traditions are largely independent of literary ones. We don't know what myths looked like in oral non-poetic forms, and there's no guarantee that either poetry or pictorial arts felt obligated to stick to those forms. Pictorial art and narrative poetry are distant cousins at most.

Notice how the website I pointed at for that 510 BCE vase identifies the figures as Aias and Achilleus: in fact there's no particular reason to read them as Aias and Achilleus. They aren't labelled, and this form of scene regularly appears with scenes showing contemporary soldiers. There's no actual reason to interpret the vase as an illustration of a myth.

Even when vases do show mythical scenes, they use their own myths: they don't emulate literary models. Very often the artists were probably altogether unaware of literary models. Here's how I put it in a thread from a few months back, in connection with depictions of Achilleus and Troilos:

The stories of Troilos and the Gigantomachy are so strongly biased towards pictorial sources that that may well be how they actually originated: as pictures, not verbal stories. ...

Pictorial artists have their own language of motifs, plot points, and story elements, and we've got no textual evidence for most of the motifs, plot points, and story elements that we see in pictorial renditions of the Troilos story.

It might be going a bit far to say that there was never an oral version of the story that used verbal language -- some extant literary sources allude to the story -- but it's a story that simply wasn't told in any literary or poetic form. There are no literary sources for Achilleus' love-offering of a hen, or the guardian snake at the shrine where they encounter each other, or the sphinx decorations on top of the springhouse, or the soldiers that Achilleus and Troilos have as companions, but these all appear repeatedly throughout the pictorial record. And, just to give you an idea of the story's importance, the Troilos story accounts for 20% of all pictorial representations of Achilleus -- without a single literary source.

At that time, for further reading on the independence of pictorial myth from literary myth, I suggested Lowenstam's book (mentioned above), and also Klaus Junker's Interpreting the images of Greek myths (2012; = Griechische Mythenbilder: Einführung in ihre Interpretation, 2005).

Edit: added link to older thread.