Kix, your question is not quite as simple as it sounds. Doing a search of "visual" on my adobe acrobat copy of VIII, Div. 1, several references to the topic arise however generally not in the context you ask. The examination part of hydrostatic or leak testing is referred to as a visual method but not in an ASME V way. In the most general terms, ASME VIII relies on NDE, such as RT and pressure testing more so than some other codes. I know this response dances all over the place but like I said your question isn't quite as simple as it sounds. There are references to that term "visual" in UG, UB, UW and elsewhere. Good luck!
With due consideration of the very good responses thus far I would say that the concise answer to your question is, no. And you will find this is typical of ALL ASME Boiler Code books.
We actually had a very good, and extended discussion of this subject a couple years ago. You might find it with a search.
I don't have a copy of Section VIII on this computer, so I cannot quote chapter and verse, but one must remember ASME differentiates between examination and inspection. Examinations, including VT, all part of typical quality control functions, are the responsibility of the contractor. Inspections, i.e., quality assurance functions, are performed by the AI.
If I remember correctly the code includes an article addressing what visual examination consists of and it is pretty inclusive. It included (based on memory) a review of material test reports, heat numbers, fabrication, welding, etc. There isn't much in the way of acceptance criteria, which is in keeping with ASME's philosophy of not dictating the means, methods, etc. of manufacturing. Even establishing acceptance criteria for visual examination is largely left to the manufacturer.
Al