In other contexts, you could use the past participle of a verb in a hypothetical statement, but not in your example as it is phrased.
For example, you could say:
You could eat the piece of fruit you chose earlier.
Here you are saying you could do something in the future, but it relies on something you already did in the past - you chose a piece of fruit in the past, but the hypothetical eating of it is in the future.
That is not the case with your example. The hypothetical roasting of a chicken can be done two different ways - you can roast it whole, or in pieces. As either option is a hypothetical action in the future, your choice of method is also in the future, so the past participle is not appropriate.