No. Two nouns next to each other do NOT indicate that they are equated. In fact, two nouns next to each other indicate that the first one describes the second one. So SuvwI' tera'ngan would probably be interpreted as "a warrior Terran" or perhaps, "the warrior's Terran". To equate the two things (as we do with "is" in English), you have to use a pronoun as verb. Thus the ghaH is required in this sentence.
The -'e' noun suffix has a few ways and location that you can use it, but it is a complex suffix and we do not teach all of its uses. Here it is doing something really unusual and there are a couple different ways of thinking of it. The simplest way is to say that when you are using a pronoun as a "to be" connector AND you have an explicit subject you MUST use the -'e' marker on that subject. There is no translation and we don't have anything similar in English, but it is required and the sentence is grammatically incorrect without it (though it's almost always perfectly clear even when you forget it).
There is a more complex explanation of why it is required, but it may be confusing for some, so feel free to stop here if you are satisfied with the above explanation.
The problem is that the pronoun, when used as a "to be" connector, is pretending to be a verb, but is not actually a verb. So it acts as BOTH the connector AND the subject. tlhIngan ghaH means "He is a Klingon." and ghaH is serving as both the subject ("he") and the verb ("is"). If we want to say who "he" is we run into the problem that we already have a subject and you can't use both a noun and a pronoun to refer to the same noun in the same place. So we have to have a way to add the subject in even though we already have a subject. For that we make it the topic by using the topic/focus marker -'e' and place it in the subject position to make it clear that we are using the topic as the subject. tlhIngan ghaH HoD'e'. Because "the captain" is acting like the subject here, we will often simply call it the subject and translate this as "The captain is a Klingon." But in reality, we are marking HoD as a topic and the more literal translation might be something like, "As for the captain, he is a Klingon."