It really comes down to your fitness and your comfort level and possibly the weather. Also it may depend on the amount of time you want to spend riding vs. looking around. I had a similar plan to yours last June, except I was camping. I also had a couple hundred miles of riding leading up to the start of the GAP. By the time I got to Pittsburgh, I had ridden four, 50-90 mile days. Not one of them had been entirely free from rain, and at least one of them had been mostly rain. Like you, I have limited vacation time, so I had a schedule to keep. But after getting to Pittsburgh, later in the day than I wanted, having also ended every other day later than I wanted, I decided to rethink my trip. I bought a train ticket from Cumberland to DC, and I rode a fairly leisurely 4 day trip down the GAP. My longest day was 53 miles. My shortest was 26. Given that the GAP was the easiest riding of the trip, I probably could have kept up my planned mileage, but I wanted to take the pressure off and enjoy my trip more, and that did it. I rode the GAP again as a credit card tour with family that fall: four days and about 40 miles/day. Very pleasant. I absolutely could have done longer mile days without the camping gear, but I found the pace enjoyable.

I've heard that the C & O gets trickier when water is added. The GAP surface seemed fairly forgiving, but I still avoided riding on it much in the rain.

I think your mileage is manageable, for me. Hard for me to say what's manageable for you. But I enjoyed taking a slower approach to the GAP. However, you stick to plan to do whole thing, given what I've heard about C & O trail surfaces, I might front-load your longer mile days. Maybe shoot for Ohiopyle on day 1 and Frostburg on Day 2 so that you can take a slower approach to the C & O if its soggy.