No. Mesh pain is not caused by an allergic reaction. It is caused by the Foreign Body Reaction which causes chronic inflammation. The foreign body reaction is part of the innate immune system and is mediated by M1 and M2 macrophages. Allergic reactions are part of the aquired immune system and are mediated by IgE. Medical researchers are experiementing with allergy testing as means of idendifying patients who will develop mesh pain. Unfortunately I think this shows a complete lack of understanding on the part of these researchers. Indicting an allergy is sophmoric and is excusable for a patient but not a medical professional.
Mesh causes chronic inflammation in all implants. But it does not cause pain in all patients. This is not surprising because this is also seen in other causes fo chronic inflammation.
There are rare cases of mesh allergy typified by an acute severe local and systemic inflammatory reaction looking exactly like an acute bacterial infection but with negative cultures and negative Gram stain.