The answer is yes for default merges. A three-way merge finds a common ancestor and then applies the differences from both sides, an operation that isn’t order dependent. The topic of merge-ordering and commutativity generated a fascinating discussion on the git list (if you’re into that kind of thing, that is). Note B into C and C into B should be symmetric, but the same cannot necessarily be said for (B into C) into A versus B into (C into A).
[Editing note, April 2020: If you add options like -X ours or -X theirs, the answer becomes “no”, and see twalberg’s answer and the others for additional caveats.]
To elaborate a bit more, based on Vince’s comment below and seh’s comment on the question, there will be two noticeable differences between B into C and C into B, neither of which affect the automatic merge resolution referenced in the question.
First, history will be different. The merge commit’s parents will change depending on the merge order. For these examples, I’m going to use “first_branch” and “second_branch”, so I can reserve letters to represent commits.
git checkout first_branch && git merge second_branch
E <- merge commit
|\
| D <- second_branch's tip
| |
| C <- another commit on second_branch
| |
| B <- and another
|/
A <- first_branch's tip before the merge
In this case, the “first parent” of E, E^1, is first_branch’s tip before the merge. second_branch is the “second parent” of the merge commit, aka E^2. Now consider the reverse:
git checkout second_branch && git merge first_branch
E <- merge commit
|\
| D <- first_branch's tip
| |
| C <- another commit on first_branch
| |
| B <- and another
|/
A <- second_branch's tip before the merge
The parents are reversed. E^1 is the tip of second_branch before the merge. E^2 is the tip of first_branch.
Second, the display order of conflicts will reverse. In the first case, a conflict might look like this:
<<<<<<< HEAD
This line was added from the first_branch branch.
=======
This line was added from the second_branch branch.
>>>>>>> second_branch
In the second case, the same conflict would look like this:
<<<<<<< HEAD
This line was added from the second_branch branch.
=======
This line was added from the first_branch branch.
>>>>>>> first_branch
Neither of these differences affect automatic merge resolution, but they do appear when you reverse three-way merge order.