No.
But you can use the links below for updates. TurboTax can help you get your returns prepared and filed. They do not have access to your account information once your returns have been submitted and accepted by the taxing agencies.
IRS processing time and refund status
The online link is your best option to track your refund. I have attached a link with more answers from the IRS as to why your refund may be taking longer to process.
Federal refund questions