No, not really. When I say something like هذا رجل (this is a man) this is enough and a complete sentence, and it has a subject and a predicative.
If I put it as هذا هو رجل it does not make much sense, unless رجل becomes defined: هذا هو الرجل (this is the man), while هذا الرجل translates as (this man). In هذا هو الرجل, the style of speech is emphatic, pointing to one specific man. Turning this "man" to indefinite, wouldn't make much sense in Arabic.
I do realize, from what I read from other users here, that some books teaching Arabic to non-Arabs do suggest the addition of هو or هي (which are pronouns) to approximate the idea of the verb (to be), because most European languages (specifically Western ones) make use of this verb to connect the subject and the predicative in a style of SVO. Arabic, is flexible and does not use the verb (to be) unless in specific manner in the past tense or in the future tense. As you saw in the early example, هذا رجل (háDhá rajulun) translates literally to (this/a man). There is no (to be) or (is) in the middle to connect háDhá and a man. Moreover, Arabic can start with a noun or with a verb interchangeably. Thus, the addition as suggested in these books, seems to be to make easy for learners to visualize the order of the sentence in a style of the naitves' languages rather than being grammatically correct.