Does a non-chiral substrate (2-bromo-2-methylpropane) also form two products via an SN1 mechanism?

If I have an alkyl halide, in which its tertiary carbon is non-chiral (for example 2-bromobutane), which reacts via an SN1 mechanism does it also produce 2 products?


I am asking because I know that the carbocation intermediate's plane of symmetry allows the nucleophile to attack equally well from either side and thus the product is a racemic mixture of enantiomers. Is this also the case for a non-chiral substrate?


