Yes, under your Pricing Rules, you can choose to automatically add the shipping rate of each item into the Product Price (and Compare at Price). If you set your rules as such, then the respective shipping rate of an item will always be added to its Product Price (and Compare at Price).
For more information on how shipping rates are determined, please read our article on How Shipping Rates are Determined.
Your default Pricing Rules are set to exclude the shipping rate from the Product Price (and Compare at Price).
Like other adjustments made to your Pricing Rules, they apply only to products that you add AFTER your new settings are saved.