Yes.  

When you setup your contact form to collect data you can add your custom fields to any of the pages that you create including the 'thank you' page. While creating your form, you'll want to make sure you click the "Yes, send a contact a thank you email." option when you first start building out your form.

While building your form, you will come to a THANK YOU PAGE OPTIONS screen that gives you two different options for your 'thank you' email. 

Note: If you choose 'Take the subscriber to an existing website address' you do not have to worry about adding custom fields.

While on this page, you can add a custom field(s) to both your 'thank you' page and your thank you email by placing the cursor in the location where you would like to place your custom field - then click the "Insert a Custom Field" button. 

Once you click on the "Insert a Custom Field" button a popup box will appear, which will list all of the fields you have created for each of your contact lists. Find the contact list where your subscribers will be added to (i.e. Event and Email Marketing Updates Custom Fields). Underneath it, double-click on the custom field you would like to insert - this will automatically insert the field into the location where you placed your cursor. When you're done, click the X box in the upper right-hand corner of the popup box.

Click the "Next >>" button. On the next screen, make any modifications that you'd like and then click the "Save" button. 

Your custom fields are now inserted in the 'thank you' page/email.