Yes, it can. All custom production is exclusive to the client, meaning the client is the only that can use the production.
When it comes to who owns the copyrights though, that is completely up to you, the customer. Sometimes customers opt to have us a supply them an exclusive licensing contract (like what you receive when you buy exclusive beats on the website), which in that manner, would require us to own the copyright so we have the authority to sell the exclusive license.
Sometimes our customers have their own contract they want us to go by which usually grants them the copyright (usually higher level custom production, i.e., major record companies, media companies like Netflix, etc).
Other times the production is simply a recreation of another song to which us nor our customer owns the copyright (use-cases for these include parodies, commentaries, etc.). So ownership of the copyright is specific to our clients needs.