Exactly. And Lincoln subscribed to his centralized political theories. The interesting thing is that Lincoln parts with Hamilton over the issue of raising arms against states in the Union.
I do not believe there would have been ANY difference except Hamilton would have been even more voceriferous. After all it was he who wrote Washington's Farewell Address explicitly warning of those who would advocate secession. It was he who happily led troops against those other advocates of insurrection in Pennsylvania. Hamilton was never one to shirk protectiong his country.
He gave his life to prevent the secessionist movement in the NE from gaining further credence. Burr's run for the NY governorship was thwarted by Hamilton primarily because Burr was running with the understanding that he would assist that movement. Burr knew that as long as Hamilton was around such a scheme would be destroyed. He just miscalculated on the massive reaction to the killing.
To Hamilton the Union was all and by 1796 he had seen the dangers posed by the demogogues attacking the federalist government. If president he would have never allowed the states to secede without doing it in a constitutional manner. Any attack on the United States would have found him first in line to resist the attackers. This is beyond doubt.