Often yes. Many drivers with these conditions qualify if the condition is well controlled. The medical examiner decides.

• High blood pressure: a driver must have no current diagnosis of high blood pressure likely to interfere with safe driving (49 CFR 391.41(b)(6)). A driver being treated may be certified for a shorter period so the condition can be monitored.
• Diabetes treated with insulin: since 2018, a driver can qualify if the treating clinician completes the FMCSA Insulin-Treated Diabetes Mellitus Assessment Form and the medical examiner certifies the driver (49 CFR 391.46). Certification under this standard lasts up to 12 months (49 CFR 391.45).
• Diabetes not treated with insulin is assessed like any other condition.

This is general information, not medical advice. Ask your medical examiner or treating clinician about your situation.