Yes, but not common. Proliferative diabetic retinopathy can cause floaters due to hemorrhage in the eye from abnormal blood vessel growth from abnormal retinal vessels (neovascularization). However, this is advanced retinopathy. Usually floaters come from changes in the vitreous in the eye (but usually between ages 50 and 70). New floaters should be checked out by a complete dilated eye exam as soon as possible.
Yes, need evaluation. Floaters in a patient with diabetes can indicate bleeding inside the eye - need to have a dilated eye exam by a retina specialist.