typically not, but several things (server configuration and firewall configuration in particular) could limit your ability to execute the command.
Try it and see 
BTW, here was a remote ping script I wrote a while back:
PHP Code:
<html>
<head>
<title>NSLOOKUP and PING or TRACEROUTE from Jason's Home Computer</title>
</head>
<body>
<font color=blue>
<?php
$shell_command = ($mode == "traceroute" ? "traceroute -I -w 2 -q 1" : "ping -c 5" );
$command_desc = "<font color=blue>" .($mode == "traceroute" ? "traceroute" : "5 pings" ) . " to $addr from Jason's computer</font><br>\n";
if (strlen($addr) > 0) {
$runext = exec("nslookup $addr | grep ame:", $output, $error);
if (!$error){
list(,$run) = each($output);
$display = substr ("$run", 6);
print "Remote Address from nslookup: $display </font><p>";
}
if ($error){
echo "Unix error code: $error running nslookup $addr<BR>\n";
exit;
}
$runext = exec("$shell_command $addr", $output, $error);
if (!$error){
print $command_desc;
while (list(,$line) = each($output)){
echo $line, "<BR>\n";
}
}
if ($error){
echo "Unix error code: $error running ping $addr<BR>\n";
exit;
}
}
print "<p><center><hr size=4 width=75%><form action=$PHP_SELF method=post><b>Enter a new address to ping:<br>\n";
print "<input name=addr type=text value=\"$addr\" size=50><br>\n";
print "<input type=submit value=\"nslookup and ping\" size=30></form>\n";
print "<hr size=8 width=50%><form action=$PHP_SELF method=post><b>Or enter a new address to trace:<br>\n";
print "<input name=addr type=text value=\"$addr\" size=50><br>\n";
print "<input type=submit value=\"traceroute\"><input type=hidden name=mode value=traceroute size=30></form>\n";
?>
<hr size=4 width=75%></center>
</body>
</html>
Edit:
looks like that was a "pre-register globals off" script, but hopefully you get the idea
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