If I were to graft two apple saplings together -- by bending the tops toward each other and lashing them together -- will the plants grow as one and benefit from one another, or will they be fighting each other for root space and light? If they would grow with each other, then I could theoretically grow a line of closely spaced fruit trees to any length, and they would be strengthened by each other in bad conditions.
There are a couple of answers to this question. Especially where trees are concerned, you can graft two or more trees onto the same rootstock, or even a single limb into a tree.
But if the graft takes, it won't behave too much more differently than just more branches of the same tree. Structurally intertwining them will not be different than if you had just taken a single tree's branches to support each other. The graft will usually only have a single set of roots, from the host tree. They will not compete. The tendency will be for the branches to grow apart so that they can independently get their own light. This is very much like any other single tree. Not sure about fusing two halves of a tree together - exposing the roots would tend to kill the tree or unsettle it.
What you describe is not grafting it is called inosculation and can prodice some truly impressive results. Inosculation can sometimes lead to natural grafting but it just as often does not. Apples are a good candidate for this to form grafting but it is not guaranteed. More importantly said trees are often competing for light so you end up having to plant more trees for the same amount of fruit, plus it is extremely time consuming.
As for strengthening that depends a lot on what you call strengthening, they may help each other structurally but joining becomes a liability for say something like drought conditions because you have a smaller root mass per tree.