Here's an approach that avoids the scary  (?{ code }) and  (??{ code }) regex constructs, but whether it's more readable than your  while loop is another question.

>perl -wMstrict -le
"my $s = '_+0GAA__+1GAA__+2GGAA__+3GGGAA_';
 print qq{'$s'};
 $s =~ s{ ( \+ (\d+) [ACGT]+ ) }
        { (my $r = $1) =~ s{ \+ \d+ [ACGT]{$2} }{}xms;  $r }xmsge;
 print qq{'$s'};
"
'_+0GAA__+1GAA__+2GGAA__+3GGGAA_'
'_GAA__AA__AA__AA_'
[download]

Note that the  '+0ACGT' sequence is handled in a way that seems consistent with your original regex, but that I don't know to be correct.

Update: Here's a version using substr that might be a bit more readable.

>perl -wMstrict -le
"my $s = '_+0GAA__+1GAA__+2GGAA__+3GGGAA_';
 print qq{'$s'};
 $s =~ s{ ( \+ (\d+) [ACGT]+ ) }
        { substr $1, 1 + length($2) + $2 }xmsge;
 print qq{'$s'};
"
'_+0GAA__+1GAA__+2GGAA__+3GGGAA_'
'_GAA__AA__AA__AA_'
[download]