You would definitely receive a 1099 but may not receive a 590 for the reasons below.
The entity or individual named on this form is exempt from the California income tax withholding requirement on payment(s) made to the entity or individual. Use Form 590, Withholding Exemption Certificate, to certify an exemption from nonresident withholding.
The 1099 is a federal form that is entered on your federal return. The information will flow to your state return. Form 590 is a California Franchise form so it would not be entered on the federal return.