I know of at least one meadery that employs that kind of technique when making some of their meads. They make a traditional, and then blend it with various amounts of different fruit wines (which they also make) to obtain the final melomel product.
While it's not exactly what you've asked about, it is a commercial example of doing something similar (ie mixing together two "complete" beverages to make a style of mead).
So, really, I'd say it's perfectly alright to do something along the lines of what you suggest. The only real challenge will be in figuring out how much to blend, and what to use, as I'm sure different braggot/cyser recipes will need different commercial beers and ciders in order to taste like the chosen style.
I wouldn't enter into a competition if you use commercial stuff though...but if you homebrew what you use, then it should be just fine.