A very similar question came up quite a while ago and I pointed out ( assuming contact of the CB is on its equator throughout this example, or at least the same through out the scenario) that while side spin doesn't (in and of itself) affect the tangent line from the point of contact on the OB, side spin can and does affect where you contact the OB in order to pocket it.
Therefore, in a tight spot (very common in straight pool) pocketing a ball that would send the CB down an undesirable tangent line, can be adjusted with side spin.
This, because now you are able to contact the OB in a slightly different spot, either thicker or thinner than the contact point with no side spin (depending on which english is used) to pocket it (turn it into the pocket) and change both the contact point and tangent line.
So, in a sort of indirect way, side spin one way or the other, can change the standard tangent line when speaking relative to the pocketing of an object ball.
It will not change the tangent line when speaking of a carom only, hitting the OB in the same spot regardless of english. Hope that made sense.