Jim,
The head can be used without the stabilizer, but having one would make life much easier. Besides providing consistent exposures, the stabilizer also provides a means of easily adjusting the exposure for dry down. For what its worth, I've used a Gra-Lab 500 timer on my Zone VI head / stabilizer combination for more than 20 years without any issues. The 505 is similar, but you would need to compare specs to see if the 505 has the same capabilities as the 500.
Hope this helps.