Will Fraxel Repair tighten very loose neck skin? The short answer to your question is no -- and here is why.
If you recognize how the skin becomes loose and how CO2 lasers affect the skin, it's easier to understand why most lasers can't duplicate surgery. Or at least why they can't provide the same level of effects.
Skin loses elasticity with age and exposure to sunlight. That's simply a given. This loose skin no longer "hugs" the framework of support tissues and sags. Fat collection in the skin can also stretch collagen fibers to further reduce skin firmness. Patients with very good elasticity typically get the best results with lipo as that stretchy skin has more capacity to "hug the curves". Think of fabric with spandex and fabric without spandex. Age breaks down the spandex. The laser assisted liposuction is said to provide some tightening as an effect of the laser, though this is typically not enough to eliminate the need for neck lift surgery.
How lasers affect Collagen and skin firmness: A CO2 laser will remove (or ablate) tiny columns of skin - this is one of the two reasons some people notice a level of skin tightening. But lasers only remove a very small percentage of excessively stretched skin. The 2nd reason the skin will tighten from laser is the collagen building response. When skin tissue is heated, as it is with laser, the body response is new collagen production and some recoiling of stretched out collagen fibers. This process also brings about some tightening as the new collagen production occurs over a number of months. But unless you have lots of "spandex" in your skin, your expected tightening is fairly limited.
Fraxel Repair (and other fractional CO2 lasers) do have some tightening effect on the skin, but they does not replace the effects of surgical procedures. For some patients, this response is greater than in others. Part of that response could be age-related as younger skin has faster and more efficient collagen-production ability.
You speak of very loose skin. You may experience some additional tightening over the next few months anyway as a response to the laser assisted liposuction, but probably not enough to satisfy you. Your surgeon is the best guide in advising what to do next.