Maybe sounds like a simplistic question, but actually worth asking because training costs money - it's an investment and like any investment should return more than it costs.
As a management trainer and coach, of course I strongly believe the answer to the question is yes, management training can and does increase profits because it increases the performance of the manager - but it is not guaranteed. A number of things have to be right in order to make it pay but I want to highlight a fundamental thing that I believe often gets overlooked.
The term management training might actually be too general and can contribute to the problem. The first question is what sort of managers does the business want? As an organisation this can be more difficult a question to answer than you might think but if a clear picture of the sorts of skills, knowledge and behaviours desired can be painted based upon what the organisation needs to make it profitable, then training can be tightly targeted and results clearly seen. Of course the rise of the competency profiling matrix in theory gives an opportunity to put down in black and white what the desired qualities of a manager should be but I would sound a note of caution to make sure that these profiles are really about what the manager should be like not just what they should know or the skills they should possess.