If you want the crystal to oscillate at its specified frequency you have to provide the correct CL. If you look at the equivalent circuit for a crystal, eg.
https://en.wikipedia.org/wiki/File:Crystal_oscillator.svg you can probably see that the value of CL helps determine the actual frequency. If the exact frequency doesn't matter, you might be able to work with what you have.
I once ordered some custom crystals for a timebase oscillator that oscillated a few hundred Hz off that of the desired frequency and there was no way I could correct it. I went back to the order form and saw that I had specified the wrong circuit. Oooops!
Cheers,