Can genes be expressed sequentially?
Simple answer: yes, this happens all the time.

A couple of notes:

Firstly, pretty much everything in biology is continuous. If a gene is expressed at a level of 1 protein per million cells, everybody would say it's not expressed, even though I guess you could argue the point. And don't underestimate how much regulation can affect expression -- you can easily have thousand-fold or million-fold differences between tissues and conditions.

Now, regarding the expression cascade: This is exactly what happens during the cell cycle. As the cell grows, there are genes that can sense the availability of nutrients and all the other signals that control initiation of cell division. Those then can turn on the genes first phase of the cell division cycle. Other regulators can sense whether that phase completed, and turn on the next set of genes, and maybe degradation signals for the genes from the first phase. And this then continues through the cell cycle.

Here's a figure from a paper that looked at gene expression in synchronyzed yeast cells (http://www.pnas.org/content/104/43/16892.full):