It is difficult to say anything about presence of ekadaNDa or it’s absence. But, we can easily say that he was not a tridaNDI.
Because, tridaNDa relates to kuTIchaka and bahUdaka type of sannyAsa which can only be accepted by tIvra-vairAgyavAn, i.e. a person who doesn’t desire son, wife, etc. in this life.
Considering that bhagavatpAda was parivrAjaka, chances of him being kuTIchaka is eliminated. Only those tIvra-vairAgyavAn persons can accept kuTIchaka sannyAsa who are unable to travel to tIrtha-xetra.
Now, considering that kuTIchaka and bahUdaka sannyAsI-s have to keep shikhA and yaGYopavIta, which are sAdhana of karma, and abide to detailed rituals as mentioned in smR^iti-s and nibandha-s, one can easily deduce that sha~NkarAchArya was not one of them.