Can cactus plants survive without stomata?

No, a cactus can't survive without stomata. Each stoma is a breathing pore whose opening is controlled on both sides by guard cells. The pores are the points of gas exchange between the cactus and the outside world. For example, the pores release oxygen, for the purification of the environment; and take in carbon dioxide, for the plant's all important photosynthetic interaction with sunlight. So the stomata control what gets into and out of the plant's stem. The point therefore is to minimize inside water losses and maximize what's needed from the outside for making energizing photosynthetic products.