Hi,
The crystal is modeled as a large inductance and series and parallel capacitances. Adding the two external load capacitors complicates this quite a bit. But even without them, you have to know the equivalent internal inductance and capacitances in order to do this kind of calculation. These parameters would be estimated anyway so you would not be able to calculate the frequency too accurately if you did. At least not for a practical circuit like you are talking about.
In theory however you can do this. You can choose a typical inductance and capacitances and also add the two external capacitors as variable capacitors. You can then calculate the frequency. By making the two external caps variable, you can study the effects of changing the two capacitors and this will give you insight as to how these two caps really make the frequency change. Most likely when you go to use this crystal in a real life circuit however you wont see the actual frequency as calculated, but you will see a similar variation as the external caps are changed to other values or even eliminated.
It's still harder to see the frequency variation with temperature using various caps though even in theory.