Yes—automatic chromatic aberration correction from a single image is possible to some extent. Many photo-oriented editors, such as Lightroom-class software, include CA reduction tools that can detect and reduce color fringing without a custom profile.

That said, it is not as predictable as correcting geometric lens distortion. Chromatic aberration depends not only on the lens, but also on the scene content and lighting—especially high-contrast edges—so there usually isn’t a single universal correction that perfectly fixes every image from a given camera/lens.

A custom profile may help, but it is less straightforward than profiling barrel or pincushion distortion. You may be able to work with specialized lens-correction software or profiling tools, but don’t expect a profile to fully eliminate CA in all situations.

So the practical answer is:

• for one uncalibrated image: use dedicated photo software with CA correction tools;
• for a repeatable industrial setup: custom profiling may help, but results will still vary by subject and lighting.