In this case, yes. The syntax you are using with your browser is probably UFT specific.
So, question first: Have you mapped your pages, etc, with your NameMapping? If not, you'll need to do some other work to do what you want exactly. Honestly, your BEST bet is to do a quick record of some of your tests to get the mapped names of your objects. Otherwise, some of those chains of objects (parent.child.child2.child3... etc) can get VERY long.
IF mapped correctly, Aliases.browser should return the browser object that you are running... under that, should then be a Page object, and then your different edit fields mapped from there. With a well mapped Page Object Model, you should be able to call something like
dim textUserName
Browsers.Item("iexplore").Run URL
set textUserName = Aliases.browser.pageSignIn.WaitAliasChild('UserName')
if textUserName.Exists
textUserName.SetText userName
textPassword.setText password
Or some such thing... probably a lot of variable definitions and syntax that I'm missing but hopefully you get the idea.
Again, for your specific test cases, you might want to do a quick record to see how the syntax plays out in TestComplete AND to make sure that your NameMapping is fully populated with what you need.