Could a larger Falklands garrison deter invasion?

Would a much stronger British base in the Falklands have prevented the 1982 invasion?

Probably. A base with substantial air, naval, and ground defences would make a full invasion far more costly and less attractive.

A serious Port Stanley base and Mount Pleasant-style air capability could deter an invasion rather than merely resist it. The historical naval party was a capable tripwire force with too few personnel for a large defensive garrison. A limited symbolic landing might remain more plausible than a full assault.