Not having a spleen would that slow down detection of HIV antibodies?

No effect. The absence of a spleen should not slow down detection of HIV antibodies as the spleen is not necessarily involved in the detection of HIV antibodies. A standard HIV test looks for HIV present in the blood and is not affected by the presence or absence of a spleen.
No. The screening test to detect HIV antibodies is among the most accurate & sensitive diagnostic tests in medicine. There is no significant change in detection of HIV antibodies in people without a spleen. All patients with HIV have a delay in the detection of antibodies following transmission of the virus. This may last anywhere from a couple of weeks to 6 months. Most tests are + by 6 weeks.