For popular cartridges that go up for "backorder" sale they ship pretty quickly. These are your .223 rem, 5.56" NATO, .308 Win, 45-70 gov, 30-30 in rifle and stuff like 357 Mag, 38 Spl, 44 Mag, etc in pistol.
But less popular cartridges may not be the case. I know some folks that are 3-4 months into waiting for the 45 Raptor brass right now.
If you're worried give them a call and just ask how long they expect backorders on 38 S&W to ship. They're super nice on the phone. If they're actively making it and receiving lots of orders it could be pretty fast, within 2 weeks like most above have reported (I've experienced this myself with most of the cartridges I listed above) but if they're just stacking backorders until they have enough to make a run and switch tooling over it could be a while.