Yes, hand-drawn diagrams are sufficient.
If the drawings in the utility application are simply better (professional draftsman quality) versions of the hand-drawn ones with no additional information, then this is fine. I have filed provisional applications with hand-made drawings.
Your drawings (and their description) should be as complete as possible in the provisional. Anything you put in the utility (i.e., non-provisional) patent application which differs from the provisional application may not be entitled to the priority date of the provisional. If the Examiner, or an opposing party in a lawsuit, asserts that an aspect or element of your utility application is not supported by your provisional application, you will have to convince the Examiner, or jury, that although the disclosures are not identical, a person having ordinary skill in the art at the time you filed the provisional application would be able to "figure out" the utility from the provisional.
If all the substance is there (as you indicate) in the provisional application drawings, then you can fix the drawing informalities in the utility application drawings. However, you should put exactly the same care and attention to detail into the provisional that you would put into a utility application. Your description in the provisional application should be clear and complete - never leave gaps or weak descriptions in the provisional application to be fixed later in the utility patent application.