Yes, we rode A14 to Mannar. In our particular case we stayed at a hotel 10km beyond the town of Mannar and hence didn't see much of the town beyond passing through it twice. So it was more about cycling the countryside including past marshes and hence that by itself wouldn't be worth a detour. We also took A32 to Jaffna. What we saw of Jaffna I would definitely put it on the list. Both A32 and A14 were reasonable roads without too much traffic. Our largest amounts of traffic in Sri Lanka overall was on the east coast and when we intersected with A02 along the south. The routes plotted by TDA generally avoided both those busier roads where they could.