Your test will be true if the variable contains at least one character from your character class. To test if the variable _only_ contains characters in your character class, you need to match from the beginning (`^`) to the end of the script:
BEGIN {
VALUE=ARGV[1];
if (VALUE ~ /^[A-Za-z]+$/) {
print VALUE " : Ok only letters";
}
print VALUE;
}
Or more concisely:
BEGIN {
print ARGV[1] ": " (ARGV[1] ~ /^[A-Za-z]+$/ ? "OK" : "BAD")
}