No, it does not work on all systems at all times.
In some it will work practically always,
on others never, on most it works sometimes
and sometimes not. I would recommend against it.

Unfortunately there is no short and sweet portable
solution. If you have or can install Gnu date it
will do it cleanly, otherwise you can find a number
of solutions posted in this group in the past.
For a general solution you could try the following,
which should work with POSIXy shells (I've only tested
it with HP's which is essentially ksh88, though):

#! /usr/bin/sh

# Date calculations using POSIX shell
# Tapani Tarvainen July 1998, February 2001 (POSIXified)
# This code is in the public domain.

# Julian Day Number from calendar date
date2julian()   #  day month year
{
  day=$1;  month=$2;  year=$3
  tmpmonth=$((12 * year + month - 3))
  tmpyear=$((tmpmonth / 12))
  print $(( (734 * tmpmonth + 15) / 24 -  2 * tmpyear + \
    tmpyear/4 - tmpyear/100 + tmpyear/400 + day + 1721119 ))

# Calendar date from Julian Day Number
julian2date()   # julianday
{
  tmpday=$(($1 - 1721119))            
  centuries=$(( (4 * tmpday - 1) / 146097))  
  tmpday=$((tmpday + centuries - centuries/4))      
  year=$(( (4 * tmpday - 1) / 1461))          
  tmpday=$((tmpday - (1461 * year) / 4))            
  month=$(( (10 * tmpday - 5) / 306))        
  day=$((tmpday - (306 * month + 5) / 10))  
  month=$((month + 2))                              
  year=$((year + month/12))                        
  month=$((month % 12 + 1))
  print $day $month $year

# Day of week, Monday=1...Sunday=7
dow()   # day month year
{
  print $(( $(date2julian $1 $2 $3) % 7 + 1))

################################# The End #################################

Those allow rather arbitrary date computations.
For example, yesterday's date can be computed like this:

julian2date $(( $(date2julian $(date +"%d %m %Y") ) - 1 ))

--
Tapani Tarvainen