Can your company deposit my refund to my bank account?

No TurboTax does not handle any type of tax refund.  Your tax refund can be direct deposited into your bank account by the IRS for a federal tax refund or your State for a state tax refund.
If you have a tax refund the bank routing and account number is entered in Step 2 of the File section after you have completed entering everything in your tax return.

TurboTax doesn't handle your refund, it comes directly from the IRS. Depending on the selection you made when you filed, it will be direct deposited or something else.