Intact bacteria will most likely be in the sediment after centrifugation. At least in clinical samples there are only very few bacteria per mL blood (depending on the age of the patient between hundreds [children] and below 1 [adults]). Following DNA extraction you end up with a high ratio of human DNA to target DNA, which in itself has a high risk of inhibition. Companies like Molzyme in Germany offer reagents and protocols to deplete human DNA from such samples and to enrich target DNA. You are right that hemoglobin is an inhibitor. However, if you extract your DNA carefully, this should not be an issue.
Thanks Oliver, that makes sense. MolYsis is in my queue, we have tested nearly all Qiagen kits and some instruments like prepito, but none of them worked perfectly so far.
It is possible to detect bacterial DNA even in serum, mostly it depends on the type of bacteria, i.e., your target. You can see the linked publications.
Article Detection of Mycobacterium tuberculosis complex infection in...
Thesis MOLECULAR EPIDEMIOLOGY OF CHRONIC BACTERIAL DISEASES IN MITHUN
we use Bioline Blood DNA extraction kit. it is working fine and we are getting very good results in PCR. we tested this kit on blood from chicken to screen for pathogenic bacteria in blood. it is few steps, simple and accurate.