Probably yes, but it will probably not help too much with human cancers.

In humans, each cancer is unique and the cancerous cells are just mutated versions of the cells of the person, so they are very related. A difficult task of the inmune system is to distinguish the normal cells, from the cancerous cells. Another problem is that the mutations in each person are different, son what is useful to cure one person may not work to cure another person.

In the Tasmanian devil case, all of them have exact same cancer. [Actually, there are two transmisible types. Most of them have one transmissible type, a few have the other transmissible type, and I guess that a small minority has it's own non transmissible variant, like in humans. To simplify the discussion, let's ignore all but the first type, and assume that all of them have the exact same cancer.] This cancer is transmissible, the cell are mutated versions of the cells of a Tasmanian devil that died many years ago. A bunch of cells go from the cancer in one devil to another devil, and start to grow. This is very difficult because the cells of the cancer are very different from the cell of the new devil, so they should be an easy identificable target for the inmune system. For this reason, transmisible cancer are very rare in mammals, there are only 3 or 4 known cases.

I'm not sure what is happening here, but a usual trick to distinguish the cells is that each cell produce some molecules that are a mix of some kind of sugar and some king of protein. There are many sugars to select and many protein parts to select, so there is a lot of possible variation. Each person produces only some of them, not every variant, so the inmune system can learn which of this are the normal one, and if it finds a cell with another combination will attract it.

This is one of the reason why organ transplant is so hard. The inmune system of the host detect that the cells in the new organ have a different variants, and start to attack the organ. This is also the reason why transmisible cancer are so rare. Even if a part of the cancer goes to another person, the inmune system of the new host will detect the unknown molecules and attack them.

Somehow, in the Tasmanian devil case the transmissible cancer can avoid this check and continue growing in the new host.

My guess of the "cure" is that some of the offspring of the Tasmanian devil mutated and get a new molecule that is not in the cells of the cancer that are like the cells of the very ancient Tasmanian devil. Or perhaps the mutation was to not build one of the molecules, or build a different variant. So the inmune system of the new mutated Tasmanian devil can learn that the old protein is not normal, and attack the cells without/with it. I'm not sure what happened here.

Once the mutant Tasmanian devil with the weird molecule survives, it increase the probability of having offspring, that may inherid the mutation, and increase the probability or survival, that increase the number of offspring, ... And sooner or later you get a world full of Teenage Mutant Tasmanian Devils :).

And, as this cancer is transmissible and all have the same kind of cells, the mutation will make the mutated offspring inmune too. [There are actually two transmissible cancers in the Tasmanian devil, so to survive they probably will have to be double mutated, perhaps they can inherit one mutation from the father and other from the mother, or a mutated one can get a new mutation.]

The cancer may also mutate to be more difficult to be detected producing the new version of the molecules, and then the devils will have to wait until one of them get a lucky mutation, and so on ...

The problem to copy this to humans is that each humans gets it own version of cancer, with cells that have the same molecules than the person. So you must:

a) Modify the cancer cells (and not the normal ones) to make them produce a weird molecule so the inmune system identify and attack them. But this is very difficult.

b) Modify the normal cells (and not the cancer ones) to make them produce a weird molecule, and retrain the inmune system to make it attack the cells with the old version of the molecule. I think this is even more difficult, or to be more precise totally impossible.