Absolutely he was within his rights to bring as many men to the capitol as he wanted – as far as we can tell, there are no limitations on the size of retinues one can bring to King’s Landing. Moreover, as Hand of the King, Ned has military authority second only to the King; he could have brought or raised as many soldiers as he wanted.
In terms of how many it would have taken to make a difference, I think at a minimum you’d need a 3:1 advantage over Cersei’s Lannister guardsmen, so about 300-350 men.