I couldn't figure out the right combination of commands to place in visudo to allow a non privileged user to check the postfix status.
Checking the /etc/init.d/postfix script it seems like the status command might call a bunch of other commands. In addition to that it seems the service is started using chroot which may be causing issues granting my account permission to check the service status.
Instead I've opted to check the service a different way. I setup the following in visudo:
# Allow the unprivileged account svchk run wc, ps, grp so that we can check if postfix is running
Cmnd_Alias POSTFIXCMDS = /usr/bin/wc,/bin/ps,/bin/grep
svchk ALL = NOPASSWD: POSTFIXCMDS
Then from my health checking script I ran the following:
ps aux | grep /usr/libexec/postfix/master | wc -l
If the results of the above command return 2 (two processes with the word "/usr/libexec/postfix/master" then postfix is running. If it returns 1 then the postfix command is not running.
I'm not overly satisfied with this solution, so if someone else has a better way of getting the actual service postfix status command to work as a non-privelaged user I'd love to hear and I'll gladly mark your response as the answer.