No, there are no benefits to giving your car throttle immediately after startup. This extra throttle will not recover the battery from the amount of power you just used to start the car any better than it will by just driving immediately after you start up. Also, given that you have a fuel-injected vehicle, there's no need to warm up the engine for more than a few seconds in the winter before driving. That some people feel the need to do this is either for their own comfort (you get hot air faster) or it's a remnant of the mindset from the days of carburetors.
Please see my response here for a similar question.
The best thing you can do for your car in the winter is start it up, scrape the ice of the car if there is any, and drive. In this short amount of time, it'll be warm enough to start driving it.