Can you put a bark collar and invisible fence collar on at the same time?

No. In my opinion, no electronic collars should be used on dogs, at any setting, except by professional dog trainers who are very experienced with using these tools to achieve a certain response from a dog. It is just too easy for an inexperienced person to injure a dog, physically or emotionally, by using an e-collar. There are much safer means available for training your dog, and if you want to provide a safe play area for your pet, build a fence around your yard.