If I started slipping, I'd be so focused on regaining control that I wouldn't be able to gauge what fraction of a second it took to engage. On the other hand, you can be sliding and if not applying throttle, not have enough wheel speed mismatch yet to engage it, which could explain the delay.
If your clutch pack is worn out, it could seem like longer till it ramps up to effective torque, but I wouldn't jump to that conclusion (yet).
4WD high is fine to use as long as you don't have any patches of dry pavement, so wheels can spin freely. I usually just keep it in Auto until slippage is excessive during acceleration (or no dry patches of pavement anywhere), and slow down lower than 20MPH on corners. I also put it in 4 high and 4 low a few times in winter just to make sure that still works including the shift motor, but 4 low just driving a short distance, slow speed then the test is concluded.