Does a standard brain ct or mri go down far enough to be able to see a chiari malformation if there was one?

Yes, particularly MR: A MRI can properly assess the craniocervical junction which is where the abnormality resides. Hopefully this eliminates your concern. Be well and wishes for good health.

Yes: Both scans routinely include the skull base and foramen magnum in order to diagnose a chiari malformation. An MRI is the better study to evaluate this possibilty.