Juliet's nurse does, in fact, give a warning to Romeo in regards to his behavior. In fact, the warning comes in two parts: the behavior and the result. Ironically, the nurse reveals the result before the behavior. It is quite shocking to hear the nurse reveal how she deals with ungentlemanly behavior (specifically of Mercutio at first):
An 'a speak anything against me, I’ll take him down,/ And ‘a were lustier than he is, and twenty / Such Jacks; and if I cannot, I’ll find those that shall./ Scurvy knave! (2.4.147-150)
It is only then that she deals with Romeo and hopes to help Juliet plan a marriage between the two. Here is how the nurse puts it:
First let / me tell ye, if ye should lead her into a fool's paradise, as / they say, it were a very gross kind of behavior, as they / say; for the gentlewoman is young; and therefore, if you / should deal double with her, truly it were an ill thing to / be offered to any gentlewoman, and very weak dealing. (2.4.160-165).
In other words, it is as though the nurse is saying, "If you are not honest and true, . . ." purposely leaving the ending open, and figuring that Romeo will remember how she deals with "scurvy knaves" such as Mercutio.
Does this warning keep with her character? Absolutely, yes! The nurse and Juliet have an incredibly tender bond that has been brewing since Juliet was born and (literally) nursed by her nurse. Of course the nurse wants to make sure that Romeo's intentions are honorable! She cares too much about Juliet to think otherwise! In fact, it would be interesting to compare the nurse's deep love for Juliet with Juliet's real mother's apathy.