Ok yes granted, that is true, but will depend on the fill factor specified when creating the index.

In the context of the question I don't think it's relevant as [presumably] the table in question that is "simple" and doesn't need any indexes will have very few rows and is probably for lookup only, so page splits wouldn't be a factor.

For page splits to become an issue the table would have to have a reasonable number of inserts performed regularly and if that's that case, it should definitely be indexed!