In terms of being accepted at an Ivy League school, does it help if a well-respected professor puts in a good word for you?
Are they writing you a letter of recommendation? I think a letter of recommendation from a well-respected professor would be a nice thing to have on your application – but only if they know you well and can speak to your personal qualities. In terms of Ivy League schools, admissions rates are so low that it probably won’t provide a huge increase in your chances of admissions.
Did you work under this prof? If so, yes. If not, then it’s of no value whatsoever.
in addition: remember, a rec letter is about YOU, not the position/prestige of the letter writer.
A sincere and enthusiastic letter from a 2nd year teacher is 5,000x better than a generic “Nicklaus has great character” from someone with letters after his/her name but barely knows you.
The latter are worse than worthless. They WATER DOWN your application.
If you have a close personal connection with the professor and he/she could write something meaningful about why you would be a good fit for the school based on first-hand knowledge then it could provide a slight bump to your application. But if the professor is a friend of a friend who you never met or something along those lines and can only write something very generic then it won’t help. In addition, I would only ask his/her help if the school is your top choice.