4.0 uses ICU regexes. (and indeed makes very extensive use of ICU in general) However, these will not be supported for regular text search, as there isn't really a good way to do index searches on regexes without writing your own regex parser. (and even then, unless you make an index that's like 8x the size of the original data you probably won't be able to make every conceivable regex search run on an index)
You will be able to filter results on regexes, so if for example you're starting from a limited subset of entries like "all HSK flashcards" you could run all of that text through a regex matcher, but there won't be any way to simply take every entry in every Pleco dictionary and run them all through a regex check in one go.
(but our new search engine is very, very powerful and a lot of the things that you might otherwise want to do with a regex can probably be done without one now)
By the way, in the Pleco Instruction Manual, the section on wildcard search ends by saying: "You can assign “$” to the Wild button instead of “@” through the Search Types screen in Settings."
Does this mean that $ is a wildcard too?