During the Crusades, many of the Assassins lived under Crusader lords and were numerous and paid very high taxes as to not get killed. The Assassins planned to convert so they could be exempt. However there plan went awry after their negotiators were murdered and they ditched all talk of conversion. If they had gone through with the plan how would their extra income and support from the Crusader lords have affected them?
I think they won't last as long as they did. If Rashideddin Sinan sends his men to try and kill Saladin as in OTL, he may decide to divert his attention momentarily from the Crusaders themselves and annihilate the Assassins once and for all.