No, this will not cause you to have any problems with Commusoft, because it is a web application and can be accessed from any computer. Although, two people cannot use the same account simultaneously even if they are on different computers. This will cause one, or both, accounts to log out.
However, if you use an accounting package such as Sage desktop, you will need to remove the integration and set it up again. Please view the relevant articles, or call/email support.