Hi Karsten,
I agree with your interpetation of the symbol you described.
See AWS A2.4-98
This example is not showing a groove weld but the intent would be the same....Look at Figure 9 on the bottom of page 18 in your AWS A2.4-98(pipe with base/cap plate seal welded all around with an 1/8" fillet). It shows the symbol "without" the all around circle and the extent of welding expected. Also an example of the same type thing "with" the all around circle included in the symbol on page 17 of the same Figure 9(for shapes other than pipe).
I agree, if the intent was not for it to be continuous, for the circumference of the pipe, a length would have been specified in the symbol.
My answer would be "no" the all around symbol does not have to be shown for that intent on pipe.
Hope this helps support your case,
John Wright