Very many years ago Jamis offered a bike that was tigged first and then had fillets laid of that. They advertised it as the best of both worlds. In reality the tig was bad and it was then covered with fillets that weren't much better and then lots of bondo to make it look good.

You may have issues with getting the fillets to flow and wet out as they should over tigged joints. It depends on what rod they used and how well it was cleaned when they welded it originally.

dave