Actually the direction of the rifling will cause the barrel to be driven on tighter due to the bullet transiting the barrel. S&W uses a right hand twist which causes the bullet to rotate clockwise from the shooters perspective. If you keep in mind the Law of Physics that states "for every action there is an opposite and equal reaction" it becomes rather obvious that the reaction to causing that bullet to spin Right is for the barrel to be spun Left.
However, barrel on S&W revolvers today are mounted with enough torque that it would be very unusual for them to loosen. I can't say that it won't ever happen, just that it's very unusual, especially in the case of the 1 piece barrels.
BTW, I have a personal "pet" theory that the reason that a somewhat larger percentage of the 2 piece barrels shooting loose is due to a mechanical interaction between the barrel and the shroud. Basically the barrel can be driven loose due to a vibration effect similar to what happens with those "electirc" football games.
Note, your 624 uses a one piece barrel, so it shooting loose would be very unusual UNLESS the frame is cracked. To check for this you will want to look and the underside of the barrel mounting in the yoke recess. The wall is rather thin in this area and when a J frame cracks it's always in this area. Unfortunately with an alloy frame failures in this area happen often enough that it's rather typical to see a post on this once every month or two. If the frame has cracked the viration from shooting can cause the barrel to shoot loose and eventually get sent downrange, so you will want to look closely.
Now for some good news. First, if you have a cracked frame S&W will replace your revolver without any argument. If you live near an S&W stocking dealer you may find that dealer will do the transfer for the replacement revolver for free. Otherwise you'll have to pay a small price to have the new revolver transferred to you.
Second potential bit of good news is that S&W will probably tighten that barrel up. However, I will warn you that with an alloy frame it is alarmingly common for the frame to crack when that barrel is removed. S&W will also tell you the same. So, I would guess that if you send your revolver in the odds the frame cracking during this correction is probably in the 5-10% range. Point is, you will want to take the time to carefully shoot your revolver from a benchrest to determine if that cocked barrel is throwing the sighting off too far. BTW, I would consider an error of 3 inches or more at 15 yards to be too much error for a J frame. If your revolver is shooting closer to the sights than this I would leave it be. Fact is that this isn't a target pistol and all you need is Defensive accuracy, not precision accuracy.
However, whatever you decide to do is your call. So if you want it fixed, or the frame is cracked, then contact S&W and arrange to send it in. BTW, your revolver has a Lifetime Warranty that S&W backs up, so if you ever find that your frame has cracked you can expect to have your revolver replaced.
