It depends on your site, so consult its meta on how to handle these. Whether you should flag them or not, or when to flag them, depends on the site.
This may be surprising, but some sites' communities actively engage in comments like this as a standard practice. Others don't. There's no network-wide rule here, and not much point trying to look for one.
Stack Exchange isn't really homogenous - different communities have different needs to properly engage in their subject matter, and different pressing issues, so Stack Exchange policy enforcement will vary a lot between sites as needed. A site making an active attempt to retain new users, for instance, would see these comments as healthy. (An ideal welcome comment might do more than just say "welcome to {site}", but welcome comments are nevertheless ok.)
The moderators of a given site may also focus their limited time on different, much more pressing matters, and thus through deliberate inaction (rather than community policy) accept these comments.
Board & Card Games does this and leaves those comments there for a while. So does Role-playing Games (such as in Can I cause a Bleeding Fullstrike with a Concussive Weapon? and If aspects are facts, are all facts aspects?). We leave these comments there for a while, and flag them for removal a while later (hours/days as appropriate) if we spot them. We also take the opportunity to make these comments useful when there's something useful to say, such as in Where Should I Start? and What materials/information would I need to construct a gameworld?
RPG.SE isn't just being lazy about their comment policy, though. Its mods and community enforce Stack Exchange's comment policies more strictly than any SE site I've seen yet. (There may be more strict, I just haven't seen it.)
Other sites will delete these comments on sight. That's up to them and their users.
