Of course! You have a lot of privacy options. You can find this under WooCommerce > Settings > Privacy Mode and Price Utils.
In the first section (Privacy Mode) you can select if you want to hide the price for not logged in users. The other options are completely independent and you can be enabled it one by one.
For more details you can see the official documentation here:http://support.ajweblab.com/docs/privacy-mode/howto.html