Can a form provide a response based upon availability in a calendar?

I would like a simple form which contains functionality to check my availability on a particular date (I am a wedding photographer). I only need the form to return a simple yes/no type answer after the person filling the form enters their wedding date. 

Is this possible with Jotform?

If I understood you correctly you want to send your users email once they submit the form to notify them if you are available on date they have selected. 

You can achieve this with conditional logic: How to Send Email Based on User's Answer

You will need to set conditions based on date that is selected. 

You will need to use DateTime field, email field and you will need to create two Autoresponder emails (one if you are available and one if you are not available). 

For example you can set your conditions like this.

Here is my demo form: https://form.jotform.com/63246183792967 

Feel free to test it and clone it. 

Other way you can achieve similar functionality is to disable dates on the form when you are not available. Inside of this guide you can find how to Use the Date Limits Option:

https://www.jotform.com/help/337-How-to-Use-the-Date-Limits-Option 

You can also use Date Reservation widget

How to Add a Widget to your Form?

This way your user will not be able to select dates when you are unavailable. I would suggest you to use Date Reservation widget. 

Hope this will help. Let us know if you need further assistance.