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probably be fine, i tigged a crack on an already very dead frame once just out of curiosity. It was around 0.6mm i reckon so middle ground in terms of thickness. Just keep the filler in/near the puddle as it can run away pretty quick. Also its probably gonna be very hard/impossible to clean the inside. The puddle will likely be pretty squirelly because of all the crap on the backside, maybe worth purging if you can be bothered as it might mitigate some of the dodgy puddle characteristics from the shite inside.
TIG welding a hairline crack in a downtube – how hard can it be? Is there more to it than running a bead over the crack? It's a pompino so won't be very thin tubing.