Does a recursive procedure "recur"?

Yes, it does recur.

According to Wiktionary, recurse is a back formation from recursion.

Google ngrams shows that recur is the base word, with recurse as a new invention.

"Recur" is the proper word for this procedure while "recurse" is technically not a word by most dictionaries. There are many verbs without an "s" at the end which gain an "s" in the adjective form. Here are some examples:

submit -> submissive

corrode -> corrosive

abrade -> abrasive

adhere -> adhesive

Naturally, "recur" follows the same pattern.

recur -> recursive

Because your function recurs, or occurs again, it is recursive.

Yes, a recursive function recurses. You can expect that a recursive function will recurse multiple times.

Here is an example in Java, that really hammers the concept home:

public void curse(){
    System.out.println("F$%& You!!");
    curse();
}