If I'm guessing what you mean correctly (sorry, that ASCII-art doesn't make any sense to me...), it sounds like it would work OK, though maybe wouldn't look the prettiest!
The joints in the tongue would clearly be a point of weakness. Joining the top and bottom of the tube to the next piece isn't much use at a corner like this - it's the sides that carry all the load at the joint. So instead of the bare joint on the left, you should add the red doublers on the right, fillet welding round the edge of them to the tubes.
This design of tongue will put more bending load on it, so be sure to pick a strong tube - it would be worth going to a 3" tube when you could keep the wall thickness reasonable - 1/8" is probably enough.