It depends upon whether the FPA is simply a read-out, or a selectable flight mode for the Flight Director Auto-Pilot.
If a display only, TAS and G/S variations will cause change in FPA. Simple pilot intervention is to alter pitch attitude as required to maintain the FPA (much as you would alter pitch attitude as required to maintain IAS).
If the FPA (or FPV) is a SELECTABLE flight mode, the F/D or A/P will maintain a constant FPA (very accurately, it's from the IRS) by varying pitch attitude to maintain as necessary.
"Now you go from zero wind to a 30 knot tailwind. Does the flight path vector increase to a higher climb angle to ensure the 3.3% gradient?" - FPA or FPV is climb angle, pitch and airspeed will vary as required to maintain the constant Climb Angle or FPA.
Caution is required as always, in climbing in any non-airspeed mode (e.g. V/S, FPA) to ensure that airspeed remains within acceptable limits. One SID that we fly on the B777 requires a 5% gradient (3.0°) to F/L 150, in this case, select the FPA at 3.0° (2.9° actually), set the required IAS to full climb speed (about 310 to 320 KIAS), and the AFCS maintains the FPA whilst the Auto-Throttle does it's best to maintain the 300 KIAS or so (which it cannot due to the steep angle, so full MCL is scheduled). The result is a climb in the vicinity of 260-270 KIAS (quite acceptable) whilst maintainiong the exact climb angle. In this way, you're getting the highest possible speed during climb (very desirable). If, as an alternative, V/S or FLCH at best gradient speed were used, climb angle would undoubtedly be higher than required, but the economics terrible (Climb economy depends heavily upon the highest possible speed right up to Cost Index Speed).
Did that help? or did it muddy the waters? I hope not!
Regards,
Old Smokey