In my own personal Fan-Fic, I wouldn't do it because it covers a heated, equal fight between an OC and CC, which would make... some people fuss, including me. The fact that it is in Championship and will interrupt the flow of the original story as well is the thing that won't make me really do it.
What do I mean by interrupting? I myself have made Alex fight Ichika, and on top of that, he'll later save both him and Houki from Unmaned Drones. But these are side events that do not affect the story at all. They might happen, but the story will go on, both cannon and the fan-fic, without modifications.
One potential problem with Laura vs Edward in a CHAMPIONSHIP match is that... well, Laura fights specific people. Among these specific people... Ed are not there. (We could wait for the anime to see if it covers the championship. If it does, then we'll have to wait and see exactly who fights who, and if any battle is not mentioned or detailed, we can then jump on it and insert our OC in there.) So we can either wait for the opportunity to show itself (if it does), or you could instead put this as a grudge battle between the two.
If you want to speak of battle statistics, Laura's IS is pretty much a very well rounded IS, versus the fragile Speedster that Edward is (well, he packs a decent punch as well). It can be a pretty equal fight. It is PLOT that will determine who wins. Not DAT PLOT, but simple PLOT.
