Greek,

You have left out some information but I will attempt to fill in some gaps to answer your question.

While you state the qualification criteria, you did not state that the job was being done to the specifications of D1.1 nor the inspections to that code.  I will assume and answer as if both are true.

You also have not stated the joint configuration, is it a T-K-Y?  Skewed angles can become another story.  We will address it as a standard 90° fit or only slightly skewed.

So, assuming the above facts in addition to your OP and comparing Welder Qualification parameters in Table 4.10, having qualified on plate for a 2G then YES the welder is qualified to weld on HSS structures of any size with fillets, PJP, and/or CJP as long as the CJP is with backing. 

If it were on pipe then the pipe would have to be equal to or greater than 24" with backing, backgouging, or both. 

He Is In Control, Have a Great Day,  Brent