Generally no. When you use the Playstation Store, you agree to pay the price shown in your cart at check-out. Whether you are a Plus subscriber or not does not matter. If the price shown in the cart is not correct, or not what you expected, then you should not proceed with the purchase. It is your responsibility to check, and it is not a good idea to agree to pay the wrong price, and then expect a refund later. This generally happens when you jump the gun on Tuesdays, and purchase Plus free content before the Playstation Store is finished updating. It never hurts to submit a refund request anyway, which has to be done by phone or live chat (https://support.us.playstation.com/app/contact_opt
I had the same thing happen to me. The game was Poker Night 2, and I downloaded it through the online browser store. When I went to the check out, it clearly showed $0.00 as the amount. I finished the check out, and a few hours later, when I looked at my email, I saw there was a charge for $9.99. I thought to myself, what was this for and then saw what the item was, and it was Poker Night 2! I contacted Playstation support and told them that I was charged for a game that was suppost to be free and showed as $0.00. They told me that they would put in a refund request. This is from an email they sent me about the refund. I am really upset on how they worded it. Basically, they acted like it's my fault and not a glitch in their system.
"Thank you for your recent call to Sony Computer Entertainment America (SCEA) Consumer Services. We have reviewed your case and as a one time gesture of goodwill we have approved your refund in the amount of $9.99. Please allow us 3-5 business days in order to finalize your refund and return the funds back to your PSN Wallet/Credit Card.
Please keep in mind that if the funds are being returned to your credit card, it will take up to 1-2 billing cycles through your financial institution before the funds will actually be posted to the account.
Please note, according to PlayStation® Network (PSN) terms of service and user agreement, all users should safeguard their account information to prevent use by any other user. SCEA shall have no liability for any unauthorized usage of a PSN account. SCEA will not be able to refund your account again. To check on your refund, please contact your credit card company."