Of course you can and as long as it's properly installed it will work great at keeping YOUR dog ON your property. What doesn't exist is an invisible fence that will keep other animals or people OUT of your yard or away from your dog. If you have a dog or a pool or some other hazard, you should really also have a physical fence. But out in the country with acres of yard or pasture, no, you wouldn't "have" to put up a real fence unless you are also keeping livestock or cattle. You have a duty to prevent your livestock from being a hazard or causing damage to others' property (eating their landscaping, digging up yards, etc.) So check with your code enforcement area which could be the county or city depending on your location and your HOA rules.
Now this is assuming that: your home is not covered by HOA rules that require an actual fence for the back yard. That would override any invisible fence you want to have. You can still have one but you'd also need a board fence. Most HOA's restrict the type of fence you can put up, ie. no chain link. And I'm not aware of any HOA's in the area that require a front yard fence and that's often the most common location for an invisible fence - you want to keep the dog in the front yard with you without putting up an actual fence.
But, again, there isn't a fence that will keep others out that's invisible.... more