Yes--this is possible and has been done, e.g.:
* DNA barcoding identifies Eimeria species and contributes to the phylogenetics of coccidian parasites (Eimeriorina, Apicomplexa, Alveolata) (doi: 10.1016/j.ijpara.2011.03.007)
* Developing an Apicomplexan DNA Barcoding System to Detect Blood Parasites of Small Coral Reef Fishes (doi: 10.1645/16-93)
* DNA barcoding and molecular identification of field-collected Culicoides larvae in the Niayes area of Senegal (doi: 10.1186/s13071-018-3176-y)
There's also a review on the subject:
* DNA barcoding of parasites and invertebrate disease vectors: what you don't know can hurt you00271-X) (doi: 10.1016/j.pt.2003.09.015)