If the WPS or Performance Qualification is qualified  vertical-up it is good for 3G-up, 2G and 1G. I would allow them to fix undercut downhill- as long as it was UNDERCUT and not a full pass ;~)
If qualified for vertical-down it is good for vertical-down only.
That is my take on it.

Roger

This is the short version: Note Vertical Down welding is not prequalified and yes vertical down welding can be used for undercut repair (D1.1-3.7.1 with restrictions) Also note D1.1-2.17 Open root welds are not prequalified, and (D1.1-3.2) GMAWs is not prequalified. With that said lets look at Table 4.1 when qualifing a WPS if you do a PQR in the vertical (3G) postion on plate the WPS from that PQR is only good for Vertical and in the same direction of travel as done on the PQR. Follow the 3G line across and it also can be used for other types of joints but all Vertical. Also see Table 4.2 for joint thickness restrictions and Table 4.5 for variable restrictions.
NOW turn to Table 4.10 The restriction for welders are NOT the same as the PQR to WPS. The weldor taking a 3G plate test would be qualified for (Follow the 3G row across) F,H, & V in both groove and fillets and more but also Vert down only. See also Table 4.11 for other restrictions. With That said you would still not have a Qualified by test Procedure (PQR) for the weldor the do any other position but Vertical.  (A WPS Problem)
More PQR testing in other position (2G see the 2G line on table 4.1 which allows a 2G test to do flat and Horizontal) would be needed to establish a qualified WPSs to do all the positions the weldor would be qualified by the 3G test (2 PQRs but 3 positions for the Weldor) Also you can follow the reasoning for the 4G position. It would be harder, but Qualify 1 PQR in 6G or Better 6GR and then a WPS could be established for Most positions then Qualify a weldor in 3G allowing Flat, Horizontal, and Vertical without doing PQRs in the other positions. Good Luck