You need to educate yourself a bit. The Arab lineage of the Nizam of Hyderabad does not trace back to the linage of Prophet Muhammad (saws). It implies a descent from 1 of the 4 rightly guided Caliphs, Abu Bakr (ra).
Intermarriage is not important here, by that logic the Ottoman Sultans were all Eastern Europeans (more or less) or Slavic. It means a degree of Arabization which is pretty much well-known among historians but that is another discussion.
Actually most of the "Turkic" dynasties were actually of Mongol origin. Including the Mughals.
Ancient Arab communities in Central Asia (Uzbekistan for instance) also merged into the wider society after a few generations which was fairly normal during those times and even is the case today.
Tipu Sultan claimed Arab ancestry as well.
As for who is Indian or not, that is up to Indians to decide, lol.
The exact date of Hyder Ali's birth is not known with certainty. Various historical sources provide dates ranging between 1717 and 1722 for his birth.
[4] There are also some variations in reports of his ancestry. According to some accounts, his grandfather was descended from a line tracing their lineage back to
Baghdad,
[5] while another traces his lineage instead to the area of present-day
Afghanistan.
[5] In a third account, written by one of his French military officers, Hyder himself claimed descent from the
Arabs Bani Hashim clan of the
Quraysh, the tribe of
Muhammad.
[6]
Hyder Ali, the father of Tipu Sultan.
Arab dynasties also ruled modern day Bangladesh and people might be familiar with the history of the Sri Lankan Moors as well.
So to reinstate what I wrote earlier, historical ties are rather deep and long predate Islam.
