<p>Does Xcode support anything akin to Visual Studio style <code>#region</code> directives for arbitrary code folding?</p>

No, you can only fold code on various defined scoping levels in Xcode.
You can use little tricks to make navigating via the function menu easier, though.
```
```
#pragma mark
```
```
Allows you to create a grouping where the label following mark will show up in the function menu. If the label is a hyphen, a separator is inserted into the function menu.
Also, the following labels in comments will show up in the function menu:
```
```
// MARK:
// TODO:
// FIXME:
// !!!:
// ???:
```
```
Obviously since #pragma mark is not really portable, if you're building a portable application and need it to work with a compiler that doesn't just ignore #pragma directives that it doesn't understand, the comment-style mark is a decent alternative.