What happens when you try it? It's pretty trivial to test...

Calling script that runs another script with system() (call.pl):

use warnings;
use strict;

system 'perl', 'call.pl';
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Script that gets called by the one above that we'll ^C (called.pl):

use warnings;
use strict;

my $c = 1;

while (1){
    print $c++ ."\n";
    sleep 1;
}
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Run call.pl to exec called.pl:

$ perl call.pl 
1
2
3
4
5
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In another terminal window, see if called.pl is running:

$ ps ax | grep called
29221 pts/9    S+     0:00 perl called.pl
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Yep, it is. Back to the other terminal:

6
7
^C
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Check if called.pl is still running after ^C:

$ ps ax | grep called
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Nope!

The whole process chain is killed when you kill the top process, unless you explicitly set the process called by system to go into the background, whether it be a daemon, service etc.

perl -wE 'say 1; system $^X, "-wE", q(sleep 1, say "\t$_" for 1 .. 10)
+; say 2;'
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but the second script terminates immediately, while the system command still runs in the background and can't be stopped by C-c :

perl -wE 'say 1; system q(perl -wE "sleep 1, say qq(\\t\$_) for 1 .. 1
+0" &); say 2;'
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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I don't know if there's a good overview of unix process control somewhere, but for starters, take a look at NOTES section in setpgid. The gory details people rarely delve into.

That said, normally your script and its descendants (or else a piped job maybe) will all run in the same process group. They are all interrupted or suspended together.