I don't specifically know about the environment in academic projects, but usually, the saying is "Hope for the best, plan for the worst".
By hiding the fact that your analysis uncovers the potential delay in getting the project done, you're essentially making it difficult for you and all others, and probably once it's delayed, it'll paint a poor picture of your judgement and execution.
Be straightforward about it, and keep everyone updated about the status as early as possible in the execution cycle. If you can make it up, good for you, otherwise, at least there will be a contingency to handle / absorb the impact of delay.
In other words, delays can happen and at times, they are acceptable, but surprises, or absolute last minute updates about missing deadlines are bad, as it costs time, money and reputation.
My advice: If you feel it's going to be delayed, mention a revised timeline and show the (re)planning on how the new dates are going to be met. This will not only take the edge of the news of the delay, but also will show your planning and commitment towards the assignment / project.