Why Vanguard's old radars might suit San Carlos

Would Vanguard's dated radar fit have made her useless in the Falklands?

Not necessarily; the task was short-range defense against non-stealth aircraft in confined terrain, and less sophisticated radars might have coped with San Carlos clutter better than North Atlantic-optimized systems.

Vanguard's Type 960, 293, and 277-era equipment was old, but the relevant question is what it actually had to detect. Argentine aircraft were not stealthy, ranges inside San Carlos were short, and contemporary Royal Navy systems had been optimized for the open North Atlantic. The caveat is not that old radar was superior in general, but that terrain and mission can reverse a simple technology ranking.