It can, and that is a known, not unusual, problem. Pain is one of the most common complications of negative pressure wound therapy (NPWT), along with bleeding, infection, and inadvertent retention of foam dressing, which can lead to infection. If a wound VAC hurts, you are not describing something nobody has seen before.
At the same time, when the therapy is applied correctly by trained professionals it is effective, leading to faster wound healing, reduced discomfort, and improved function. Both are true. Pain is a known complication of a treatment that is, taken as a whole, meant to reduce discomfort — which is a reason to report it rather than to accept it as the price of the therapy.
Pain around the edges, where the seal sits on your skin, has its own fix. If skin breakdown or localized pain develops around the site of negative pressure application, topical emollient therapy may be used, or an alternative nonadherent dressing can be placed under the transparent adhesive sealant tape. That step is for the person applying the dressing, not for you. What it tells you is that something can be done — which makes it worth saying exactly where the pain is: in the wound, or on the skin around it.
Two other complications can show up as discomfort: hypersensitivity reactions to dressing materials, or maceration due to excessive moisture. Maceration is skin that has been wet for too long. Again, the point is that these have causes that can be found and changed.
This article can’t tell you how much a wound VAC will hurt, or whether its dressing changes are worse than any other kind. What is clear is that monitoring should be continuous: regular wound assessment should include checking for any discoloration, duskiness, or mottling of the wound bed or wound edges. New pain is a reason to have the wound looked at, not a reason to wait for the next scheduled change.