It will but I am unsure of the cooking time as cucumbers are not the same as zucchini. Just be sure that it is cooked but not over cooked. Like not mushy.
When the jars are sealed they last months. And because of the vinegar and such it can last a long time in the fridge after opening. Not sure exactly how long since the jar empties before it ever goes bad but it does last quite a bit. I'd say over a month for sure.