You are talking about cutting a branch off a tree and then putting it back on? This would be similar to grafting and it could be done (probably the branch should not be bigger than a pencil). If you are talking about doing this with the trunk itself of the tree, then no, it could not be done and really the amount of time doesn't matter.

Interesting and creative idea but it won't get you any awards from tree-lovers. Cutting the trunk damages the cambium layer which feeds the tree. The dead interior wood might not mind (although it serves as structural support for the tree) but you would still be stifling a portion of the tree's feeding system and creating a potential point of entry for disease. This might work if you do not damage too much of the cambium layer but there is risk to the tree with this idea. I dont' know if it's likely that the reinserted piece of cut cambium would knit back into the main trunk but I doubt it. Adding the "ashes" (which is really the ground up remaining bone chips if my understanding is correct) to a planting hole might work depending on what kind of tree it is (you would need to research the particular species' requirements, strengths and weaknesses). I'd be curious to hear what an arborist or horticulturist has to say about all of this.

If you wanted the jar to be in the tree you could get the tree to totally surround it. This may take a while though, similar to getting a barbed wire fence growing through a tree...
Or you could but it down into the root ball, and the tree would naturally surround it.

It would be best to choose a fast growing tree. Willows grow fast, and I assume they would heal fast too.

If the crematory jar was made more into a tube, the tree could easy be trained to grow around it, like the fence, and totally encapsulate in over time.
The trick then would protecting the container and making it look semi-decent while the growth process is taking place.

THE BEST IDEA however, would be to grow the tree specifically to be used for such a situation around a decorative with a lid facing outward. This way, the crematory jar could simply be placed into the tree whenever the death occurs in the family. The cover of the tree box could be part of the memorial, or it you really wanted, it could manufactured out of glass once the tree finished encapsulating it. do you like that idea? Go ahead and use the idea if you like. You would need to make the side walls of the box very strong, possibly with a domed top, or have a triangle box to support the weight of the tree that will grow above it....

Good Luck!