Yes, Diabetes patients can donate blood, as normal people do.
In fact, blood donation improves insulin sensitivity and aids in better glucose control, as observed in many epidemiological studies.
The mechanism is the reduction in ferritin stores (without compromising haemoglobin levels) leading to low free iron levels which catalyse the production of reactive oxygen species (ROS).
ROS accumulation aggravates insulin resistance, and henceforth their depletion is beneficial.
After blood donation, HbA1c (glycated haemoglobin ) may be underestimated for a limited period due to the increased turnover rate of red blood cells.
This caveat should be noted before interpreting/ordering the former test.