Does the term "abusive" connote intent?

This question simplifies a complicated issue. To normal people outside of a situation looking in, yes, of course all abuse looks like it comes from malevolent intent. If people could be completely honest with themselves, then they too would would see malevolent intent.

So, as Josh correctly answered, yes, there is ill-intent behind all abuse.

But your question is does the term "abusive" imply that the individual harbors malicious intent?

The answer is not always, because individuals don't all have the advantage of wisdom and clear perspective from which to judge their motives.

The definitions given below imply strong actions which tend to break rules and laws. I'd say that in performing them you are very likely to be supposed of being aware of what you are doing.

Abusive:

• Characterized by improper or wrongful use: abusive utilization of public funds.
• Using or containing insulting or coarse language: finally reprimanded the abusive colleague.
• Causing physical injury to another: abusive punishment.
• Relating to or practicing sexual abuse.

Source: www.thefreedictionary.com