Does the use of business management software improve IT management?

It could be but not necessarily.
If one uses IT for business then for sure it improves the management otherwise both management are different.

IT Infrastucture managment software and Business management softwares will vary depends upon the requirement. If buisness managment software have all modules of IT Infrastucture then it will be helpful to improve.

it's regarding to organization size, but i's necessary to improve IT management also to control and mange how the IT is work and mange the requests and incident or problems that facing users or systems, also to coordinate with users and IT technician, So it's neccessary also regarding to ITIL and problem management

It is not very clear that what do you meant by business management software!!! Do you mean an ERP? CRM? PLM? May be these softwares enables more business productivity, not used for IT management. IT becomes and an integral part of these softwares, becuase it is IT that Sets up, administer, maintian these softwares. These softwares runs on different pllatforms and infrastructure. IT Management software is used to manage thee platforms and infrastructure. May be we can manage IT in an AD Hoc way without IT Managment softwares as well, but effort spent will be very high. In some scenarios, IT management softwares becomes very essential. For E.g A network management software gives you complete picture of the your network. A System managemtn software gives you complete gives picture of your servvers and other systems.

Not Necessarily.
Any software is just a tool, if those who are using the tool are not convinced it is helping them, or they are not trained enough to handle it .......etc.
It will not improve anything, actually sometimes things turns to be worse.
Introducing any new tool should be part that might be needed, or might not be needed, as part of a business change that should be justified, supported by management and well planned to make sure the expected benefits are realized through continuous monitoring,control and stakeholders involvement.
In other words, thinking of the tool should come last, not first.
You've to answer why to change, then look at the hows, what and when.

Yes: Any technology supports Of course used for Improvement only.As you can think the rule of technolgy changes and impact of changes existed now in world.We can quote many examples ....for Examples How many peoples are using the INLAND Letters in writing now?????

IT management is one of overall business function and business management off course covers IT as well. Now it's no more two apart things but inegated ones. If you may specify some case, we may able to help you in better way that which particular IT management function you want to perform in which business management software.

Bizz management software will differ from IT in many ways.
However you will find common grounds.
But not a good idea to depend on it entirely.
IT is entirely a techno driven environment.

if you have skills , it will be more add help ?

Yes, and that is the whole point of IT.