Assuming AWS D1.1:2006 then Table 4.11 on Page 146 states that a welder qualifying on 3/8" plate is qualified for 1/8 to 3/4" with a footnote, "d". Footnote "d" reads, "Also qualifies for welding any fillet or PJP weld size on any thickness of plate, pipe or tubing."

...So, based on footnote "d" I'd say that Yes, that person is qualified to make fillet welds on plate over 3/4" thick.