Is having your hands "on the hoods" of drop handlebars safe for braking?
I commute every day in SF with drop bars. It's not an issue for me. You quickly adapt to the hand position, if you bike is set up in a way that is comfortable for you.

The real safety issue you should be worried about, IMHO is not braking itself, but rather the "heads-down" position you can be in on the bike itself. You have to get used to looking around you/behind you for cars, etc. That's why your position/comfort on the bike is so important. 

You can also install cross/interrupter levers for a second braking position option, usually at a nominal cost (not sure if this works with your particular breaking system).