G-forces [1] are a consequence of acceleration. An accelerating object will experience g-forces in an atmosphere or in a vacuum. ("Drafting" [2] is an aerodynamic process by which a following object exploits a leading object's slipstream to reduce the former's drag.)
With a slingshot, the destructive force is the g-force inflicted by the acceleration. (With a rocket, the destructive forces are mostly vibrations and aerodynamic stress.)
Note that a slingshot doesn't require lots of Gs. One could use a super-long slingshot to achieve the necessary velocity. But super long is super expensive, so high Gs it is.
Very long cables are a lot cheaper than very large slingshots?
Anyway just thinking out loud.
Unless your cable were elastic, this would not materially change the payload's acceleration. That said, you might find skyhooks [1][2] interesting.
Would it be possible and useful to do it with a 2 payloads system: one dumb piece of material first which can take lot of G followed closely by your "fragile" payload using its draft?