Review Objective
If your objective is to get into testing as quickly as possible, there is probably no way to convince you to do a review before compiling. This attitude, however, confuses speed with progress. Although getting to testing would seem like progress, the testing time for defective code is highly unpredictable, and for large programs it can take many weeks or months. If you measure your overall performance both with reviews and without, you will find that by reviewing first, you may take a little longer to get into testing but the testing time will be much less.
Conversely, if your goal is to remove the maximum number of defects, you will want to do the code reviews when they are most effective. The compiler is equally effective before or after the review, so if you find any of the defects it would miss, you are ahead. My preference is to review the code before compiling and then use the compiler as a check on the quality of my code review. If the compiler find more than a very few defects, I probably have a quality problem and need re reexamine my review practice. This is also a good guide for then to update your Code Review Checklist