You'd hold onto your cash like grim death and only spend when you absolutely had to. This causes a decrease in demand which leads to sellers lowering prices (ie, the value of the dollar goes up more), falling production, hence more unemployment which creates the vicious circle. This really happened, guys, it's not just some grumpy 70 year-old technophobe banker that doesn't get it.
I am assuming that you don't think this is totally irrelevant, so by your line of thinking, even if dollars were not a monopoly back then, the end result would be the same. After all, since it's a time of absence, people would desire to save, and they would hold on to the deflationary currency, even if they had an alternative. Actually, they would convert the alternative to the deflationary one, causing more deflation.
However, this line leads to another type of irrelevancy. If a monopoly is not needed for a deflationary spiral to happen, without Bitcoin, people would just buy precious metals, land or some other possibly deflationary commodity. In such times, hoarding is what happens.
So I think I have successfully proved that this thing doesn't have to do anything with Bitcoin. Please tell me if I haven't.
So, what remains is whether a deflationary spiral at all is possible without a monopoly on money supply, and if it is, is Bitcoin helpful (since it cannot be harmful). This would be a more sophisticated discussion though.