No. There is no evidence from clinical trials or from the field following worldwide use of currently available COVID-19 vaccines that COVID-19 vaccination causes any type of immunosuppression in any population group.
It is not possible for COVID-19 vaccines to cause AIDS, which is caused by the Human Immunodeficiency Virus (HIV). Suggestions that COVID-19 vaccination can cause a similar immunosuppressed outcome, which some have dubbed “VAIDS”, are not based on any observed or reported evidence.