Draupadi is mentioned in two verses of Thirumangai Alwar's Periya Thirumozhi, a collection of his poems. First of all there is this verse from his poem Virperu Vizhavum, in praise of the deity of the Parthasarathy Krishna Temple:
andanan Siruvan araSart am araSarku
iLaiyavan aNiyizhaiyai Senru
endamakku urimai Sei ena tariyAdu
emberumAn aruL enna|
Sandam al kuzhalAL alakkaN nooTTruvar tam
peNDirum eidi noolizhappa
indiran Siruvan tEr mun ninrAnai
The blind king Dhritrashtra’s son, king of kings Duruyodhana, and his younger brother Dusshasana went to the beautiful jeweled Draupadi and said, “Serve me”, Unable to bear this, the dark tressed one prayed, “Lord, save me!”, when Lo! The lord took her grief and gave it to the others’ wives, making them lose their marriage thread. He drove Indra-born-Arjuna’s chariot. I have seen Him in Tiruvallikkeni.
Then there is this verse from his poem Anrarar, in praise of the deity of the Thiruneermalai Vishnu Temple:
tAngAdadu Or ALariyAi avuNan tannai
veeDa munindu avanAl amarum
poongOdaiyar pongeri moozhha viLaittu
aduvanriyum venrikoL vALamaril |
pAngAha mun aivarODu anbaLavi
padiTTraindiraTTippaDai vEndar paDa
neengA cheruvil niraikAttavanukku
iDam mAmalaiyAvadu neermalaiyE ||
The Lord came as a terrible man-lion with Uncontrollable rage and killed the angry Hiranya, dispatching his flower-decked queens into the fire. Then in the victorious war, he befriended the five Pandavas, killed the mighty hundred and protected Draupadi’s fair name. Tirunirmalai is His great hill abode.
Now only the first verse explicitly refers to Draupadi's act of Sharanagati, but I'd argue that the second verse alludes to it as well, insofar as Krishna "protected Draupadi's fair name" as a reward for her Sharanagati.