Not sure about which Perumal prasadam your query is related to. After Mahalaya paksha tharpanam, we usually partake prasadam that was offered to our house Perumal during Tiruvaradhanam.
If the query is about partaking temple Perumal prasadam – since one is expected to partake palaharam after tharpanam, if the prasadam given is of palaharam category, one can partake that; but if the prasadam happens to be made of rice such as Puliyodharai, Dadhiyannam, etc., it is not partaken. On that day, food must partake only during the daytime, and fasting is observed in the evening. Those who are unable to fast, are allowed to partake palaharam, but if it happens to be made of rice, it must be avoided.