boxstarter/Web/InstallingPackages.cshtml gives an example of using BoxstarterConnectionConfig:

$cred1=Get-Credential 'MyTargetMachine\myusername'
$cred2=Get-Credential 'Domain\myDomainUser'
$result = (new-Object -TypeName BoxstarterConnectionConfig -ArgumentList machine1,$cred1),`
    (new-Object -TypeName BoxstarterConnectionConfig -ArgumentList machine2,$cred2) |
    Install-BoxstarterPackage -PackageName MyPackage

BoxstarterConnectionConfig actually takes three parameters, and the first parameter is a connection URI (http://machine1:5985/wsman), not a hostname like in the example. If you enter machine1 you get an instant failure connecting to "".