It depends on the autoimmune disorder. MS is an autoimmune disorder that doesn't show up in blood work at all; rather it shows in spinal fluid. Diabetes presents immediately in blood tests that are fun for glucose tolerance, etc. There are two specific tests for Lupus, both of which must show positive for a definitive diagnosis.
In modern science and medicine depending upon the type of bloodwork being done, this process can take a matter of minutes, hours, or in some cases even days. It all depends on what process and equipment is being utilized.