Yes, there would have been an uprising even if the company had withdrawn the Enfield rifles.
Explanation:
Actually, the rising started from Meerut in May 1857 however a lot of this occurred in Bengal at Barrackpore in March 1857. An Indian soldier named Mangal Pandey said no to the use of greased cartridges with animal fat so he was hanged. He became the first martyr of freedom struggle in India.
Hindus believed that one should not eat beef (cow meat) since cow is their holy animal. The Muslims successively believed a pig is dirty and one should not eat pig.
The new cartridges introduced by the British was coated with layers of cow or pig fat initiated the spark of the uprising and paved the way for the great revolt 1857.