your answer is absolutely correct and you have elaborated it quite well.

Sindh is indeed babul is islam not becaz M.B.Qasim came here with his army to subdue this place but becaz ummayed rulers had their own vested interests there.And they had attacked this sub continent severel times before muhammad Bin qasim.And sindh being a port was their launching pad.it was a gate way for them.They entered india only by this way and becaz of that it is called the gateway of Islam.it was indeed beside being a gateway of india too.

Thanks umar...