$200 is a very low price for a competition, so do check it out. Does that cover just what you'd have to pay the pro? What about entry fees, etc? Are travel expenses (for you and pro) involved?
I do comps on the cheap and one I travel to costs me a minimum of $1500-2000. So if $200 is your total cost, go for it!
If you did decide to dance with the beginner (is it really fair to her to expect her to dance silver if she's a beginner?), I think you should take lessons together between now and the comp so that you can train and develop together and dance as a partnership at the comp as well as possible.
As far as your lead is concerned, seems to me it could go either way. It could be that you are having to make concessions to your beginner's lack of following skills, or it could be that your pro's advanced following skills compensate for some deficiencies in your lead that show up when you lead someone less skilled. I know I certainly follow my pro better than anyone else, but I don't consider following him to be a real assessment of my following skills. I sort of average out how I follow everyone I dance with to see how well I'm following overall.