Not easily with the <ol> tag that I'm aware of.
However, you can achieve your goal using the counter-increment and counter-reset properties in CSS2
I'll look at those links - they're CSS properties I was unaware of.
It was more out of curiosity as I can easily have the list as a series of styled paragraphs and just not type the period/full stop:
1 First item
2 Second item
and so on.