I have trained (and raced) sick. I think the trick is that you just want to be careful when the sickness moves down to your chest (congestion) from your head (stuffy nose) because you can exacerbate the issue by taxing your body with a run … especially a marathon! So go see a doctor (if you haven’t already) and get some good drugs to knock it out.
There are thousands of runners who have ran marathons or IRONMAN distance races while sick. If you think ahead and train/race smart, I don't think there will be much issue. When training, I would just keep your pace slow and easy. I would lay off tempo and speed workouts until the last week before the race but keep the distances based on the schedule so you keep mileage and time on your legs (just run EZ). If you must get in some speed, short efforts at race pace will help with your muscle memory and form before getting out on the course.
When you get out there on race day, I would follow your race plan, run at the pace you had planned on, and FEEL where you need to be on that day rather than making up your mind to be slow weeks in advance. The important thing is to be true to yourself and listen to what your body is trying to tell you. I mean, if you need to walk... it's OK, just walk.
I would say the biggest challenge when trying to run when feeling under the weather is largely mental. As you know, endurance sports can play tricks on your psychological stability and coming off a sickness in addition to two weeks of rest will wreak havoc on your psyche. When you hit mile 20 or 21 you will start thinking about how all the bad things that have been out of your control have held you back. So, you’ve got to mentally prepare for that in advance so you don’t end up convincing yourself to walk off the course. You might be thinking there is no way that could happen, but you will be dealing with an oxygen starved brain and muscles that are craving rest not to mention that 800lb gorilla that hopped up on your back… it can happen.
As long as there is no chance of you catching pneumonia, I say go for it. Your training will pay off. Taking time off when your sick is okay, you won't lose too much training with 2 to 4 weeks off.
I once flipped a coin to run either the ½ or full marathon in Austin. I lost the coin toss and ran the marathon with 15 miles as my longest run. By mile 20 or 21 my legs were in full spasm and when running down the finish shoot I couldn't bend them because they were locked. I finished in 3:30 but before the melt down I was on pace for 3:07. At the end, I was hobbling the final 2 miles near 10:00/mile pace but I would not let my brain (or better judgment) convince me to quit.
So see your doctor and make sure running won't kill you. If the doctor gives you the "all clear", get back to training and have fun at your next race.