I'd say that Monica Cellio's answer is a must-have here and I strongly recommend reading her answer, which I fully agree.
Interestingly, that question (over at Meta SE) is exactly about mods posting welcoming comments here, on Italian SE, so that question and this one are actually dupes IMO.
Monica's answer isn't all that comprehensive, but IMO it's straight to the point, so I'll just put my summary here:
Small communities need to grow, when retaining new users is an important role in their growth. And because the easiest way to drive off a new user is to ignore the person, welcoming comments, despite often being found chatty by experienced users, are quite important actually.
Adding to what DaG has answered, such "guidelines" against chatty comments need NOT be enforced consistently across different SE sites. That it works well on SO doesn't mean it will also work well on smaller sites like us (Italian Language).
Oh, and the actual question you're asking about: I think welcoming comments are suitable for deletion after some time, such that most users should either see it or become unlikely to return, say for example, a month or more would be good. And as a consequence of my agreement to Monica's answer, I'm actively against deleting welcoming comments preemptively. Italian SE is a small site and we need new users to feel l'accoglienza we have. (Of course, one is suitable for deletion if there're two - there's usually no need to pile them up)