That depends on what you mean by "affect your profile".
If you mean whether or not the downvotes will have a lasting influence, well sure. They will remain there and any rep lost will remain lost. But if that is the only negative blip within your participation, the subsequent upvotes you receive on other questions/answers will largely outweigh this one negative question. Downvotes also weigh far less than the rep gained from upvotes. So if highly downvoted questions are not a regular occurrence for you, then its effect will disappear over time.
If you mean whether or not this highly downvoted question will have a lasting effect on how people perceive your contributions, then that depends on what you do after that. Most users however will not look any further than either your current contribution, or your overall reputation. And believe me, there are several users I am aware of who persistently contribute poor content and still seem to gain several thousands of rep points.
And even if they look at your profile, if you have a significant number of contributions, the most negative ones will sink to the bottom, while your best contributions will come to the top. Sure, one can always find such contributions if they explicitly look for them. But if the contribution is old and buried among several good contributions, I would be more inclined to think "Well done, he has improved over time" rather than "Ha gotcha, I knew he sucked". :)
So all in all, if you learn from your mistakes and contribute enough good content afterwards, though perhaps annoying to you, the net-effect of your downvoted question will be minimal.