Find if at least one element of a group matches at least one pattern

I have a vector of several regexes. They are so short and so different that it is not worth trying to make a single regex that captures all of them at once.

I also have a data table with two columns, one contains strings, and the other an ID, with multiple strings per ID.

What I need is to find out for which ID, there is no match between at least one of the associated IDs and at least one of the regexes.

MWE:

icd10.autol.tr.regex <- c("C91\\.00", "C92\\.00", "D61\\.\\d{1,2}", "C91\\.10", "C92\\.10", 
                          "Q82\\.8", "D76\\.1", "C81\\.\\d{1,2}", "E76\\.0", "C90\\.00", 
                          "C94\\.60", "C85\\.9", "Q78\\.2", "D59\\.5", "D57\\.1", 
                          "D56\\.\\d{1,2}", "D82\\.\\d{1,2}", "C86\\.4", "C93\\.3\\d", 
                          "C91\\.6\\d")

codes.to.check <- data.frame(code=c("E85.3",  "C90.00", "Z45.20", "N08.4",  "Z29.21", 
                                    "Z52.01",  "C79.3",  "Z45.20", "F05.9",  "B99", "A04.7",  
                                    "R63.3"), 
                             id=c(1,1,1,1,1,1,2,2,2,2,2,2))

Here, I want the result to look like

ID  result 
1   TRUE      #because we matched C90.00
2   FALSE     #no match 

If I had the list of possible codes as strings, I would have used %in%. For regexes, I tried using str_extract from stringr, but it doesn't seem to take vectors for the serched pattern. I guess I could do nested loops with str_extract, but this feels inefficient. Is there a more idiomatic way?