will it be possible for my wife and I both to arrive in Saudi Arabia at the same time prior to me starting work
Generally NO.
will she really have to remain at home waiting for me to arrange a visa for her?
Generally YES.
The process is that the company sponsors you and provides a working visa, once you arrive in Saudi you then obtain an "Igama" residence visa, if your salary is above a certain limit, you can then sponsor your own wife and family. The whole time to do all of this can be measured in weeks or months!
Mutt