Improving Flyback DCM Peak Power using CCM
Quasi-square-wave quasi-resonant converters also called QR converters are popular structures in ac-dc chargers for notebooks and portable electronics. They are popular because:


they operate permanently in discontinuous conduction mode (DCM).
they remain a first-order system easy to stabilize despite a right-half-plane zero located in high frequency (versus a low-frequency one in CCM).
you can approach zero-voltage switching or valley-switching operation if you reflect enough voltage to the primary side at turn-off. Excellent for switching losses and also for the radiated EMI.
you can use "lazy" diodes in the secondary side as the diode spontaneously or naturally turns off when the core is demagnetized. This changes from CCM where the hard-blocking event generates losses in the primary and secondary sides due to the reverse recovery charge of the diode. QR avoids this problem and also avoids shoot-through current when a synchronous rectifier is used. QR was popular for this reason some time ago in cathode-ray-tube (CRT) TVs and their 120-150-V high-voltage rail where you could not use a Schottky diode.
they naturally offer an excellent protection against short circuit as the operating frequency will go to an extremely-low value (long demagnetization time), naturally scaling down all switching losses. Something you don't have at fixed \$F_{sw}\$ where you would enter a heavy CCM in short circuit engendering extra losses with possible runaway of the peak current and clamping network.


Now some drawbacks:


variable frequency: there is no clock in the simplest version and a QR converter is a self-relaxing system. The frequency depends on load and line conditions: low frequency at low line and high power, high frequency at high line and low power. Efficiency suffers in light-load conditions and that is the reason you now find systems that fold the frequency back via a voltage-controlled oscillator (VCO) taking the lead in moderate to light-load operation.
large power capability in high line: this is really the plague of the QR operation and I wrote a series of articles in How2Power.com showing how you need to reduce the maximum peak power capability at high line compared to low line (see the below picture):




The first article of this 3-part series is here.

3.large circulating rms currents compared to CCM. The fact that you transmit power in DCM implies large secondary-side current requiring the selection of good-quality capacitors. Same in the primary side with more losses in the copper, the MOSFET but also in the core considering the large flux swing compared to the smaller minor loop in CCM.

So, as you can see, many arguments to adopt or reject a QR converter. Now, back to your questions regarding possible saturation in CCM. No, you can't saturate in the case you mention because the transformer is designed to accept the maximum peak current the controller limits the primary current to. Whether the converter operates in CCM or DCM does not change, the maximum peak won't be exceeded as it is under control cycle-by-cycle. Of course if volt-second balance is violated for extreme duty ratio conditions, saturation risks exist but that is a different story.

Now, how can you pass more power in CCM than in DCM? Actually, for a given design at a fixed switching frequency with a given transformer, you will pass more power in DCM than in CCM. The general power formula for a flyback converter is: \$P_{out}=0.5\times L_p\times (I_p^2-I_v^2)\times F_{sw}\$. For a given maximum peak current set by the controller, you see that if the converter enters DCM at a high voltage input, the term \$I_v\$, the valley current, no longer subtracts from the peak value and you transmit more power. This is the over-power phenomenon I described in my series of articles.

For the QR controller you mentioned, it is possible to increase the delivered power by turning the variable-frequency QR controller into a frequency-controlled converter and increase the switching frequency without exceeding the maximum peak current set by the controller: when the switching frequency is too low or when the feedback voltage exceeds a threshold, you decide to quit QR operation and no longer wait for the core total demagnetization to impose new cycles of smaller periods. In the above formula, if the frequency increases, then the converter operates in CCM with a low valley current and you can safely increase the delivered power. But you suffer higher switching losses and lose valley-switching operation. If this is temporary as for an in-rush demand, not a big deal and quite convenient as you do not need to thermally-size the entire converter for a 2x power since it does not last.