NO! It does not. The command:

Code:

LogDate="$(echo "$4 $5" |
		sed -e 's/\//-/g' -e 's/:/ /1' |
		tr -d '[]' |
		date '+%s')"

and the command:

Code:

LogDate="$(date '+%s')"

will both set LogDate to the current time as a integer value specifying the number of seconds since the Epoch. I repeat: The date utility does not read from standard input! The echo, sed, and tr utilities in that pipeline have absolutely no effect on the value returned other than that the time needed to start those three additional processes might delay response by a second or two depending on your hardware and system load.
I repeat: The code in red above is shell commands; not awk commands. Sticking shell commands inside the action section of a BEGIN clause in an awk script does not make them awk commands. THIS WILL NOT WORK!

I understand that you want to prepend a reference date and a reformatted version of the date from a line at the start of some lines in your log file. Processing would be hundreds to thousands of times faster per line if we can put the timestamps at the start of the line as YYYYMMDDHHmmSS instead of as seconds since the Epoch, but it isn't easy to get the seconds between the two from this format. I repeat: Do you NEED the number of seconds between these two timestamps on each line?

The script that I posted:

Code:

#!/bin/ksh
awk -v RefDate="$(date -d'now-2 second' '+%s')" \
	-v LogDate="$(date '+%s')" '
{	print RefDate, LogDate, RefDate-LogDate, $0
}' "/var/log/httpd/rewrite.log" |
grep -B 1 -A 0 -inP '(rewrite\s+.?assets/.+.?\s+->\s+.?sites/default/files/.+.?|rewrite .?sites/default/files/.+.?\s+->\s+.?assets/.+.?)'

should produce exactly the same output as your 1-liner did. If you changed your 1-liner to use now-3 hours instead of now-2 second, you can also make that change. It will affect the timestamp printed in the awk output, but will not affect anything else. I can't verify that they are equivalent because date on my system does not support the -d option you're using, the input you have given me does not contain any lines that will be matched by your grep command, and the RE you're using with grep is not supported by the grep I'm using; but I'm sure they will produce the same output if given the same input at the same time.

It's well past my bedtime, so I'm going to bed. Please post a more complete sample of your log file along with an answer to the above question about the need for the difference between the two timestamps when you get to work later this morning and I'll take another look at it this afternoon.