I'd like to deposit my tax refund into my Fidelity Investments account. That's not a checking or savings acct, but does have routing and acct numbers. Can I do this?

Yes you can.

To deposit your refund into a single account

If you are depositing your federal income tax refund into only one account, you can simply fill out the two lines in the refund section of Form 1040 or Form 1040A. Your account number and routing number.