They will know it's lowered. I am on pro kits and people who don't know anything about cars ask me about my "lowered" car or say something about it.
I have never done a trade in so I can't really answer your question. However, do you have your stock springs/shocks (if you swapped your shocks)? If so, you can always negotiate that. You know what it costs to you so take what you want for your car, minus that $200. If they feel differently, spend that $200 and go back. I know that is hard when you are buying a new car but I have bought two cars for an unreasonably low price by walking away (it wasn't exactly my intention to buy either, but they became affordable enough for me to do so).
I will say that when I was buying my Accord, they were taking quite a bit off of a V6 I was looking at because of the fact it had aftermarket wheels and exhaust. I don't know if they discounted it off the bat or that nobody was buying it but they subtracted $1,500 off the sticker price in the window and made sure I knew that I was getting it cheaper. The rims were not bad but not particularly attractive and the exhaust was just welded on mufflers (not CARB legal, they shouldn't have been selling it that way), but $1500 was off the price. This was in 03 and the car was really clean and low mileage, lease trade in. Not sure if it was Certified or could be, for that matter. An equivalent V6 was about $1500 more.
Again, never traded in a car so I really don't know, that's just what I saw at a Honda dealer when our cars where pretty close to new. At a regular used car lot, you see them trying to either up the price, or at least play up the "premium features" if you look interested. On older cars, I rarely see much of a difference in price from a used dealer unless the modifications are extremely low end (ebayed out Hyundai's and the like).