following LanX's steps

$_ = q(aaa; ; bbb ; "ccc ; ddd ;"  ee;e  ";"  fff ;);
s/(".+;.+"|;)/$1 ne ';' ? $1 : '&&'/ge;
[download]

outputs

aaa&& && bbb && "ccc ; ddd ;"  ee;e  ";"  fff &&
[download]

so It fit the authors task, if he doesn't have any
of these constructions:

; " ; " ; " ; " ;
[download]

seems to me that, these should be processed with toggles =_=
LanX's code for the author's task:

$b = 0;
$_ = q(aaa; ; bbb ; "ccc ; ddd ;"  ee;e  ";"  fff ;);
$a = join '', map {$b =!$b if /"/; s/;/'&&'/ unless $b; $_} split //;

output:
aaa&& && bbb && "ccc ; ddd ;"  ee&&e  ";"  fff &&
[download]