Yes, the branches will flower and bear fruit (provided it's not too hot for pollination to be successful).

If height is your only worry, you can simply let the top of the plant hang down when it gets taller than what's supporting it. What kind or staking or cage are you using, and how tall is it?

Here's the FAQ on blossom drop, which tells how temperature affects the tomato's ability to set fruit:
http://faq.gardenweb.com/faq/lists/tomato/2000083030027695.html

I don't think I am going to have any problems going forward with heat, unless our weather changes dramatically from what it has been so far, so I look forward to new fruiting for at least the next couple of weeks.

The beefsteak is about 5 1/2 feet tall currently. It is in a 4 1/2 foot tall cage (i know, bad planning) with some bamboo staking (about 5 1/2 feet) supporting the main stem. I am getting some good downturn on side branches, but the main stem is about at the top of my stake and still growing straight up. And that unfortunately is where my flowers are forming. I am worried if I pinch that to restrict further upward growth, I really won't have any more buds.

I think you could attach an extension to your existing bamboo stake using a pair of hose clamps. I've never tried this because my plants in Maine never get very tall.

Fred