Almost all of the comps I have entered require that your beer entries are received 1 or 2 weeks before the comp is to be judged. So if you have one week to get them carbed and another subsequent 1 or 2 wks before the judging, then you should be pretty okay to have the beer properly carbonated.
On a side note, I have repitched some fresh champagne yeast (lalvin EC-1118) to help speed up carbonation. On a 7% beer I have gotten carbonation in 4-5 days using this method keeping the bottles aroun 75 deg F.
So check and see when the actual judging will be and you should be okay. I have shipped beers that I just bottled several days before the entries were due and the bottles were carbonated just fine by judging time. Fine enough to medal anyway!
