I'm in the southern hemisphere, so we are one month into summer
now. But there has been a lot of wind here over the past few
months, seriously thrashing the garden.

Where are you that the wind is so bad? Is this abnormal?

Anyway, one tomato plant had a section broken off of the top.
The detached piece is maybe five inches of the central stem, with
some leaves.

If I put it in a glass of water, can it start growing roots?

Go for it. It's your best option.

Is the main plant likely to regenerate, or to bypass growth
around the injury? Especially considering that it was the
central stem that got broken?

My peppers did.

Dick