UPDATE: This is my 100th post! :))

Yes, but think about buffering. Perl won't flush it's buffer until it sees a newline.
You have no \n after the <br>, so this is what happens:

1. perl fills the buffer
2. perl sleeps for two seconds
3. perl appends to the buffer, and then flushes it because the end of the script is reached.

Which of course is not what you want.

You could put a \n after the <br>, or turn on the autoflush using $| = 1 (often seen obfuscated as $|++).

print "First<br>\n";
sleep 2
print "Second\n";
###
$| = 1;
print "First<br>";
sleep 2;
print "Second";
[download]

I recommend the newline solution, because HTML doesn't care about the newline being there, and autoflushing decreases performance.

Information about $| and many other special variables can be found in perlvar.

2;0 juerd@ouranos:~$ perl -e'undef christmas'
Segmentation fault
2;139 juerd@ouranos:~$
[download]