What would happen if I combined this polymer and this metal (assuming I can)
You can combine materials in two ways: chemically and mechanically.
On average, if you want to the desired physical properties to add up, you want to go mechanical way, not the chemical one.

Once the reaction takes place, the there is absolutely no reason to assume the product preserves properties of both precursors. It might sometimes, but more often than not it's a completely different beast.
Speaking of retaining physical properties in terms of logic and addition operation, in chemistry both $\text{true} + \text{true} = \text{false}$ and $2 + 3 = -42$ are possible.
Mixing water and sodium won't result in liquid metal.

What you probably want to look into instead is mechanical combination, or, more precisely, composite materials such as fiberglass or carbon plastics alternative where titanium would act as a 2D or 3D supporting mesh for sorbothane, though not reacting with it chemically.
Such poly-phase materials are already used for monolithic composite armor plates.