Ask pre-college program teacher to write your recommendation letter for university?

Yes, unless the application materials require that the letter be from a teacher of a regular semester class.

However, for the letter to be of much help to you for admission, not only should it include information as to your excellence in all aspects of being a student, but it should also make clear that even though the writer's contact with you was in a summer program, the writer spent as much or more time with you as a would a teacher in a regular semester class.

You should not discuss this or any other aspects of the contents of the letter with the writer unless you are asked by the writer what to include. It is insulting to do so unless you are asked, in which case you should be prepared to point out the matters that will be most helpful in making you stand out as an excellent student and candidate for the university.

However, the teacher will know of this criterion and will decline to write the letter if not enough time was spent with you. I include this information not only to guide you as to what not to say, but also to explain why your request might be declined.