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Edit: more about being non-blocking.

There is normally no reason for you to use delay() at all in your program. The only reason for this function to exist is to help complete beginners write their first blink-the-LED program. As soon as you start writing anything non trivial, you should ban it from your vocabulary. The Blink Without Delay tutorial is here precisely to teach you how to get rid of delay() by using millis().

In this particular case, however, the drawback of delay() may not be too severe: if the alarm is sounding and you delay a tone change, you may hear it as a glitch that breaks the rhythm of the sound. If the delay is short enough, maybe up to 10 ms or so, you are unlikely to notice it. Longer delays will be noticeable, and it's up to you to decide whether you find them annoying or not.

It is possible to ensure a very steady rhythm despite the delays by using interrupts, but this will cost you your 16-bit timer. Or you could write your own implementation of tone() that does both the pin toggling and the tone changes using a single timer. Any such option will require you to learn about low-level timer programming, which is significantly more demanding than learning to use millis().

Edit: I just wrote (but did not test) a non-blocking version of this alarm, based on a state machine and the timing technique from the Blink Without Delay tutorial. Here it is, as a class:

class TwoToneAlarm {
public:
    static const uint16_t HIGH_FREQ = 3300;
    static const uint16_t LOW_FREQ  = 3000;
    static const uint16_t TONE_DURATION = 200;

    TwoToneAlarm(uint8_t output_pin)
    : state(OFF), pin(output_pin) {}

    // Start the alarm.
    void start()
    {
        tone(pin, HIGH_FREQ);
        state = HIGH_TONE;
        last_tone_change = millis();
    }

    // Stop the alarm.
    void stop()
    {
        noTone(pin);
        state = OFF;
    }

    // Call this periodically to handle the tone changes.
    void update()
    {
        if (state == OFF) return;
        if (millis() - last_tone_change >= TONE_DURATION) {
            switch (state) {
                case HIGH_TONE:
                    tone(pin, LOW_FREQ);
                    state = LOW_TONE;
                    break;
                case LOW_TONE:
                    tone(pin, HIGH_FREQ);
                    state = HIGH_TONE;
                    break;
                default:
                    break;
            }
            last_tone_change += TONE_DURATION;
        }
    }

private:
    enum { OFF, HIGH_TONE, LOW_TONE } state;
    uint16_t last_tone_change;
    uint8_t pin;
};

It could be used like this:

TwoToneAlarm alarm(8);

void loop()
{
    if (some_scary_condition()) alarm.start();
    if (some_other_condition()) alarm.stop();
    alarm.update();
}

Note that the whole program must be non-blocking (delay()-free), otherwise the tone changes will not be done on time.

You can just have a variable that remembers whether the alarm is supposed to be on or off. Let's call it alarm_on. Then:

bool alarm_on;
static void start_alarm() { alarm_on = true;  }
static void  stop_alarm() { alarm_on = false; }

void loop()
{
    if (alarm_on) alarm();
    if (some_condition()) start_alarm();
    if (some_other_condition()) stop_alarm();
}

For a better approach that allows you to sound the alarm without blocking the whole program, see the Blink Without Delay Arduino tutorial.

You can just have a variable that remembers whether the alarm is supposed to be on or off. Let's call it alarm_on. Then:

bool alarm_on;
static void start_alarm() { alarm_on = true; }
static void  stop_alarm() { noTone(); alarm_on = false; }

void loop()
{
    if (alarm_on) alarm();
    if (some_condition()) start_alarm();
    if (some_other_condition()) stop_alarm();
}

For a better approach that allows you to sound the alarm without blocking the whole program, see the Blink Without Delay Arduino tutorial.