Well, not in principle. The donated eggs come from young, healthy donors, mostly under 30 years of age. The likelihood of these eggs accumulating genetic mutations is low and therefore amniocentesis is not necessary even if the recipient mother is of advanced maternal age. Combined first-trimester screening is usually done because it does not present any complications or risks.
In spite of everything, it is always advisable to follow the instructions of the doctor responsible for the control of the pregnancy.
Suggested for you: Amniocentesis: Indications and Possible Risks.