Depending the temp where you lock them in it can take a bit for engagement.
I think you don't use a lot if any grease on the locking part of the hub as the grease gets hard in the cold and it will be hard for the gears to lock.

As for how far I have never seen it written anywhere on just how far.
Because the gear is spring loaded and it may not line up just right is why they want you to move a little so the gears can line up and engage.
So it can be as little as an inch or a mile if the grease is holding the gear back from moving.

On trucks I had locking hubs on I would lock them in at first snow and keep them locked till spring when we would not get any more snow.
I would just need to move the lever inside from 4x2 to 4x4 high and be in 4x4.
During the rest of the year when unlocked I would put the transfer case in 4x4 low hubs unlocked and run across a long parking lot just to keep the oil coating everything inside the case.
The truck I have now does not have locking hubs so during the non-4x4 season I would flip the switch to 4x4 low and go straight across that long lot, tank it out of 4x4 low turn around and do the same back to the other end. Now that I live in the south and not much need for 4x4 I could not tell you the last time I had it in 4x4, I should look into this.

BTW with the hubs locked and say driving on roads and find you need 4x4 you can shift it into 4x4 high, shift on the fly, as long as none of the wheels are spinning.
To shift into low range you MUST STOP, take trany out of gear shift transfer case to 4x4 low and trany back into gear. NO shift on the fly for low range.

It may use a little more fuel with hubs lock but it will not hurt anything with them locked. The truck I had with the locking hubs had 230K when I sold it and 4x4 still worked, just tired of the truck.
Dave ----

 

What Dave said. If you notice at all that you are still in 2WD after locking the hubs and shifting into 4WD, then something is wrong. Most likely it's that you over-greased the hubs. When you get a chance take them off, wipe essentially all of the grease off them and put them back on (don't use carb cleaner or anything to get ALL of the grease off, just wipe off all but a thin film). Like that they will drop in as soon as it lines up, and if it seems like it's in 2WD it's lining up probably over a dozen times for each time the back tires spin.

 

Your supposed to use white lithium grease in the hubs, not a wheel bearing grease.
If the springs are good, just rolling forward or reverse 1' should engauge the hubs. (when in "lock")

 

When they are right, the hubs take only a few degrees of rotation before they lock, especially of you ease into it when you start out. I have one that is getting a little stubborn on my 89 and it takes a few rotations of the rear tires before it will lock in, I need to check it. I would only use wd 40 on the hubs. And make sure there are no burrs on the teeth. Hard to believe the whole thing relies on a little pot metal toothed sprocket in there.

 

Yep that is why when I raced 4x4 off road we would ditch the locking hubs for full time hubs, all steel gears and locked in "full time"!
Dave ----