Like any home state senator, he'd be a favorite son candidate and take votes from everyone. And except for his idiocy on amnesty and immigration, Graham is mostly a conservative. - He'd have no chance in other red states because his amnesty positions would kill him, but not in his home state.
And he might well win the primary, particularly if the Dem race is not very competitive and Dems decided to crossover and vote from Lindsey to cause mischief (open primary state). Some think many Dems vote for him as senator since there is little chance of a Dem winnning in SC.
The point would be to prevent Cruz or any conservative from winning the first conservative state primary, and thereby gaining momentum and becoming a frontrunner.
That’s probably a fair assessment.
As a point of reference, let’s remember that Lindy did NOT deliver SC for McCain in ‘08. Gingrich won SC and that was his “last hurrah”.