'complete' is an ambiguous term. There is actually no such thing as a 'complete' blood test. If you're asking if it is possible for a blood test to reveal that you are taking steroids, the answer is, of course, yes. If you're asking if it is standard practice for most jobs, the answer is no. Hormone levels will generally not be checked, unless you're applying for a job where steroid use would be of concern to your employer. Generally, an employer would have no incentive to pay for this to be tested.
'Government job' is also ambiguous. Are you applying to be a mail carrier? A clerk? Or are you applying to be an FBI agent? These are all government jobs, but the drug tests they give will vary immensely.