Of course it's possible. It depends on the specific circumstances. For example, if you are planning on having a starting gravity of 1.055 and you end up with 4 gallons at 1.055 and then add 1 gallon of water, your starting gravity will be considerably lower and "overdiluted" in reference to your recipe. It doesn't even have to be that extreme, though. You could have 4.75 gallons at 1.055 and you add 0.25 gallons of water, and you've still over-diluted it since you were shooting for a starting gravity of 1.055 and your 0.25 gallons of water got it below that, even though you probably won't be too much below your target. If you're talking about "too much water = too little malt/hop flavor," that really depends on the recipe. I mean, you could probably do 0.5 gallons of super concentrated malt and hops and then add 4.5 gallons and still have a decent gravity and "reasonable" IBU, but it would be super diluted from what you originally boiled. Whether it would taste okay or not... I'd have to try it out to say for sure (since I haven't done anything like that before), but I'd imagine you could match your values in your recipe... :/
Very case-specific, but yes, it is definitely possible.