The answer to the question in the title depends on how much humidity your home deals with during the summer. If you don’t normally experience extremely high indoor humidity (relative humidity higher than 70%, although some people find more than 60% uncomfortable), then your AC will be able to keep you cool and happy. The air conditioner is not exactly controlling the humidity—although it’s doing some dehumidification—but it doesn’t have to work hard against humidity to deliver a comfortable environment for your house.
If high humidity is a problem you often encounter during warm weather, then it’s unlikely your AC can do much about it. It can provide cooling, but it won’t make a noticeable effect on humidity because an air conditioning system isn’t equipped to do that job.