Was the work of Sri Sankaracharya completed?

Chaos pervaded all through India in the matter of religion and philosophy. Sect after sect, such as Charvakas, Lokayathikas, Kapalikas, Shaktas, Sankhyas, Buddhas and Madhyamikas sprang up. The number of sects rose as high as seventy-two and there was constant conflict between sects. There was superstition and bigotry. Darkness prevailed over the once happy land of Rishis, sages and Yogins. 

Some of the recognized threats to Dharma during this time are summarized as follows:

1. Foreign invasions by Greece, Turkey and other Middle Eastern countries.
2. Corruption of Sanatana Dharma due to various reasons
   1. People who did not follow the full import of Vedas propagated their own religious methods, which were based mainly on rituals.
   2. Ignorance of Vedas even by the intellectuals of those times due to the complex language of the Vedas.
   3. Religious ignorance of majority of people because they did not know Sanskrit.
   4. Popularity of the Vamachara of Thanthric practices leading to other cruel practices such as Nara Bali.
3. The launching of the Buddhist and Jain religions. Both these religions were based on the spoken languages of the masses, and opposed the cruel form of religion as popularized by followers of Thanthric methods. This made them more attractive and intelligible to the people of the time than the corrupted form of Sanatana Dharma.
4. Many of the great Hindu kings like Asoka and Harsha were attracted to religions other than Sanathana dharma.

Such was the state of the country at the time which just preceded the birth of Sri Sankaracharya.

http://www.hindupedia.com/en/Adi_Shankaracharya

Sri Sankara was born in a very poor family  in a village named Kaladi, six miles to the east of Alwaye, Kerala.  

The period at which he was born was not clearly known.

Many scholars fixed and adopted the  788 A.D as his year of birth and some others put it at  509 BCE.  He met his end  in his thirty-second year.

https://www.booksfact.com/history/adi-shankaracharya-birth-year-509-bce.html

Sri Sankara ascended the seat of omniscience after inviting Vedic scholars from all parts of India and answering their numerous questions. Sri Sankara, by vanquishing all the religious opponents of his day-and they belonged to no less than seventy-two different schools-and establishing the superiority of the Vedic Dharma, had become the Jagadguru of all.

Sri Sankara's success over the other religious sects was so complete that none of them have since been able to raise their head in the land. Most of them have disappeared altogether. After Sri Sankara's time, although a few Acharyas have appeared, none of them have been able to vanquish those who differed from them as Sri Sankara did and establish unquestioned supremacy.

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Coming to the question: Was the work of Sri Sankaracharya completed?,  I doubt whether Sri Sankaracharya left the world after completing his task!  

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Sri Sankara was acknowledged as Shanmata Prathisthapaka.

Shanmata  meaning "Six Religions" in Sanskrit. While these the different Religions of  initially had separate followers,Sri Shankara, , worked to join the adherents of the different Religions into one through spreading his Advaita Vedanta philosophy. 

Adi Sankara's followers worship one divine power, Brahman in all its six manifestations. It centers around the worship of the Six of the supreme Deities of the different religions/ways of worship,ie., Shiva,Vishnu, Shakti,Ganesha, Skanda and Surya  as One. This is based on the belief in the essential oneness of all deities, the unity of Godhead, the one divine power, Brahman.

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Was his success over non-vedic systems and unifying the different religions into ONE, made his task completed?

I doubt it.

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Sri Sankara was an acknowledged Advaiti, and thus, his thoughts follow that of Vedic way of life.

It is a well known fact that in Vedic age, the Almighty God was worshipped in different forms, depending upon the manifestation of the power of the God.

1.  Indra, Vishnu, Vayu, Agni, etc, were different forms of manifestation of the power of the God.

2.  There was no Idol worship in Vedic Age.

3.  We can find Rudra in Vedic age, but not Shiva as in the form that is known to us now.

4.  Vishnu was regarded as one of Adityas, but not as the Supreme God.  

5.  Shakti and Ganesha were not in Vedic Age.

Though Sri Sankara, an Advaiti,  might have Idol worship of different deities ,ie., Vishnu, Ganapati, Shiva, Shakti, etc, for the time being and for the sake of unifying people, he might  have tried to direct the people towards Vedic way of life, had he lived further.

Unfortunately, he died at an early age, according to the DIVINE Plan.

So according to my assessment,another gigantic personality, like Sri Sankara, will appear on the horizon, to complete the task of Sri Sankara, in directing the people towards Vedic Way of life.