Как я могу программно проверить, присутствует ли клавиатура в приложении для iOS?

I think you need to use the notifications that are provided about the keyboard:

From: http://developer.apple.com/iphone/library/documentation/UIKit/Reference/UITextField_Class/Reference/UITextField.html

Keyboard Notifications

When the system shows or hides the keyboard, it posts several keyboard notifications. These notifications contain information about the keyboard, including its size, which you can use for calculations that involve moving views. Registering for these notifications is the only way to get some types of information about the keyboard. The system delivers the following notifications for keyboard-related events:

* UIKeyboardWillShowNotification
* UIKeyboardDidShowNotification
* UIKeyboardWillHideNotification
* UIKeyboardDidHideNotification

For more information about these notifications, see their descriptions in UIWindow Class Reference. For information about how to show and hide the keyboard, see Text and Web.

Create a UIKeyboardListener when you know the keyboard is not visible, for example by calling [UIKeyboardListener shared] from applicationDidFinishLaunching.

@implementation UIKeyboardListener

+ (UIKeyboardListener) shared {
    static UIKeyboardListener sListener;    
    if ( nil == sListener ) sListener = [[UIKeyboardListener alloc] init];

    return sListener;
}

-(id) init {
    self = [super init];

    if ( self ) {
        NSNotificationCenter        *center = [NSNotificationCenter defaultCenter];
        [center addObserver:self selector:@selector(noticeShowKeyboard:) name:UIKeyboardDidShowNotification object:nil];
        [center addObserver:self selector:@selector(noticeHideKeyboard:) name:UIKeyboardWillHideNotification object:nil];
    }

    return self;
}

-(void) noticeShowKeyboard:(NSNotification *)inNotification {
    _visible = true;
}

-(void) noticeHideKeyboard:(NSNotification *)inNotification {
    _visible = false;
}

-(BOOL) isVisible {
    return _visible;
}

@end

Код drawonward очень близок, но конфликтует с пространством имен UIKit и его можно упростить использовать.

@interface KeyboardStateListener : NSObject {
    BOOL _isVisible;
}
+ (KeyboardStateListener *)sharedInstance;
@property (nonatomic, readonly, getter=isVisible) BOOL visible;
@end

static KeyboardStateListener *sharedInstance;

@implementation KeyboardStateListener

+ (KeyboardStateListener *)sharedInstance
{
    return sharedInstance;
}

+ (void)load
{
    NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
    sharedInstance = [[self alloc] init];
    [pool release];
}

- (BOOL)isVisible
{
    return _isVisible;
}

- (void)didShow
{
    _isVisible = YES;
}

- (void)didHide
{
    _isVisible = NO;
}

- (id)init
{
    if ((self = [super init])) {
        NSNotificationCenter *center = [NSNotificationCenter defaultCenter];
        [center addObserver:self selector:@selector(didShow) name:UIKeyboardDidShowNotification object:nil];
        [center addObserver:self selector:@selector(didHide) name:UIKeyboardWillHideNotification object:nil];
    }
    return self;
}

@end