Yes, but it will be difficult to get accurate measurements due to the limited resolution and quantisation noise of the average scope (I am assuming you are using a digital scope and it is not one of the super-expensive high-resolution models).
You could get more accurate measurements with a scope that has a differential comparator input. You use this to offset the nominal Zener voltage from the measurement so you can view and measure small deviations from that offset voltage. AFAIK such capability is not available in modern scopes and you have to revert to an old-fashioned analog scope e.g. Tektronix 7000 series with a 7A13 differential comparator plug-in.
The most accurate way to measure the Zener voltage under pulse conditions would be to use a a high-speed digitiser such as found in high-end bench multimeters or data acquisition systems. This could be triggered to take a fast measurement or series of rapid measurements a short time (allowing for the Zener voltage to settle) after the current is applied to the Zener.
Alternatively, you could build your own test system using a fast ADC, 14-bit or better, paired with the micro of your choice.