Going based on the person who coined the Constant Interface pattern an anti-pattern, I would say although you don't intend the client(s) to implement the interface, it's still possible, possibly easier, and shouldn't be allowed:
APIs should be easy to use and hard to misuse. It should be easy to do simple things; possible to do complex things; and impossible, or at least difficult, to do wrong things.
Although as mentioned below, it really depends on the target audience
A lot of easy-to-use designs patterns get a lot of criticism (Context pattern, Singleton pattern, Constant Interface pattern). Heck, even design principles such as the law of demeter gets criticised for being too verbose.
I'd hate to say it, but these kinds of decisions are opinion based. Although the context pattern is seen as an anti-pattern, it's apparent in mainstream frameworks such as Spring and the Android SDK. It boils down to the environment, as well as target audience.
The main downside that I can find is listed as the third listing under "downsides" in the Constant Interface wiki:
If binary code compatibility is required in future releases, the constants interface must remain forever an interface (it cannot be converted into a class), even though it has not been used as an interface in the conventional sense.
If you ever figure "Hey, this actually isn't a contract and I want to enforce stronger design", you will not be able to change it. But as I've said, it's up to you; maybe you won't care to change it in the future.
On top of that, code clarity as mentioned by @TagirValeev. Interfaces have the intent of being implemented; if you don't want someone to implement the API you're supplying, don't make it implementable. But I believe this revolves around the "target audience" statement. Not gonna lie, I'm with you on the less-verbose foundation, but it depends on who my code is for; wouldn't wanna use a constant interface for code that may get reviewed.