Note Canfield:"The Mughals- Persianized Turks who invaded from Central Asia and claimed descent from both Timur and Genghis - strenghthened the Persianate culture of of Muslim India.".  So, yes their army was probably Turkic speaking and even the language of the army was probably Turkic.  But the language of culture was Persian and it was Persian culture that was spread in India by these Persianized Turks.  Note my also other response just above where I expand in more detail on the issue.