It is not needed to have a browser service on the network, however the function required to ennumerate a list of domains relies on this function. The function will build a list of available domains and compare the domain entered during the credential configuration to this list to see if is valid. If you know the domain of the account is availble you can simply click next as it is only a simple check, and not an error.
We build a list of domains available by calling a windows API call, WNetEnumResource. We then compare the input of that last line to the list to validate if the domain is available.
This technet article describes the call: http://msdn.microsoft.com/en-us/library/aa385449(v=vs.85).aspx