Vehicle battery (NMC) max discharge rate
But will it be able to support that huge current without any voltage dip?

All chemical batteries have internal resistance / impedance. Any current draw will introduce a voltage drop. Due to construction and chemical effects there may be some variation in internal resistance and it is likely to increase at high currents.
Parameter 5.3 on the datasheet you linked specifies that the internal impedance is &lt;= 73 mΩ. At 1000 A that would introduce a voltage drop of 73 V. Since the battery is 3.7 V this is impossible. If the impedance remained at 73 mΩ at high current then you would have a 50% voltage reduction (1.85 V) at \$ I = \frac V R = \frac {1.85}{0.073} = 25 \ \text A \$.