This should be possible, although I haven’t used the CSV export extension myself.
According to their documentation, you can add custom meta keys to the export.
The plugin saves the customer’s input as a custom meta field with their order. The custom meta name that you would use would be the title that you entered on the Conditional Field’s settings page.
Again, I haven’t used the export plugin, so I’m going off of their documentation only. It seems like you would simply enter the CSV’s column heading, select “Meta field…” from the drop-down menu, then type the meta key in the box below.
Using the example in the screenshot on the link I provided above, “CustomerIP” would be replaced with what you want the column heading on your CSV file to be, “Meta field…” would be what you would select from the drop-down menu, and “_customer_ip_address” would be replaced with whatever you entered as the Title field from the Conditional Checkout Field settings. Enter it in exactly the same as it is in the settings (i.e. don’t add hyphens or underscores if there is a space in between words).