In the case of TrueType hinting with the interpreter, it can. The SCANTYPE instruction [1] allows the hint program to request different scan conversion settings. It's mainly used to change the dropout control mode. Without dropout control, the rule is strictly that pixels whose centers are inside of the glyph are drawn. At small scales, this can lead to features smaller than a pixel disappearing, so dropout control adds additional rasterization rules to draw some pixels even if they're slightly outside of the glyph. I've seen that FreeType supports them, and I'm sure it must have a complexity and performance impact on them. Granted, it's less useful with antialiasing, but is still a case where hinting affects the rasterizer's operation.
In any case, hinting just changes point positions. It doesn't affect the way the rasterizer works at a fundamental level, I don't believe.