Answer: It will not regain its shape, because when it is corked it can not replace the volume of material that you just take out of it.
Step-by-step explanation:
When you squeeze the bottle, you are changing the volume of the bottle, in this process, you are "expelling" the material inside the bottle.
When you stop squeezing, there is a change in pressure, and the bottle "absorbs" air, until the pressure is equilibrated, and in this process, the bottle returns to the original shape.
Now, if you take the sauce out of the bottle and immediately cored it, then you removed the material inside of the bottle and did not let the bottle to "refill" the empty space with air, so it can not regain its shape.