The answer is yes (assuming the base metal thickness and diameter of the production weld is within the limits established by the performance test). Refer to QW-356 for GTAW and QW-353 for SMAW.
The P number for welder qualification is an essential variable (QW-403.18), however a test performed on P1 does qualify the welder for a variety of base metals, including P5B.
The F number is essential (QW-404.15). In your situation, the F number for ER70S-2 and ER90S-B9 is the same (F4), as is the F number for E7018 and E9015-B9 (F6).
The fact that the perfomance test was performed without backing gas means that the essential variable related to gas is not applicable in your situation (QW-408.8). It is only applicable if you test with gas and wish to delete backing gas in production (not allowed). You are allowed to add backing gas if you test without it.
Charles Hall