dispatch_once is not reentrant. Use a NSReentrantLock if you want reentrancy.

dispatch_once_reentrancy_test.m

#import <Foundation/Foundation.h>

static NSRecursiveLock *_lock = nil;
// constructor = run before main. used = emit code even if the function is not referenced.
// See http://gcc.gnu.org/onlinedocs/gcc/Function-Attributes.html
static void runBeforeMain(void) __attribute__ ((constructor, used));
static void runBeforeMain(void) {
    _lock = [NSRecursiveLock new];
}


static void test(void) 
{
    static NSUInteger count = 0;
    NSLog(@"iteration #%lu", ++count);

    // YES = deadlock after a reentrant call using dispatch_once
    //  NO = allow reentrant calls using NSRecursiveLock
    BOOL deadlock = YES; 

    if (deadlock){
        static dispatch_once_t token;
        dispatch_once(&token, ^{
              test();
        });
    } else {
        [_lock lock];
        test();
        [_lock unlock];
    }

    count--;
}


int main(int argc, char **argv) {
    @autoreleasepool {
        test();
    }
    return EXIT_SUCCESS;
}

Makefile

CC=clang
CFLAGS+=-std=c99 -g
LDFLAGS+=-framework Foundation 

dispatch_once_reentrancy_test: dispatch_once_reentrancy_test.o

Does this address the issue with using @synchronized(self) within a singleton while code elsewhere could also being using @synchronized(singleton_instance), causing a dead lock?

While dispatch_once doesn't have this problem, like you mention it is not reentrant.