Fitting the freewheel will have no effect on the adjustment to the bearings. If it doesn't take at least "a couple of goes" you're either lucky, very skilled, or have set yourself a low 'smooth rolling' standard.
I've changed out rear bearings quite a few times and I've never once got it right first time.
When I change out bearings on a freewheel axle, I remove the locknut and cone from the non drive side and pull the axle out from the drive side. I then make sure that the cups (the innards of the hub) are spotless (no grit or dirt).
There is no need to do anything with the drive side nut and cone other than to make sure that they are locked up tight and that the cone isn't damaged. If the cone or whole axle needs to be replaced, I set up the drive side with exactly the same amount of spare stud protruding from back of the drive side locknut as on the original axle (I put the old and new axles side by side to check this).
It's then simply a case of putting the greased new bearing cage the right way around on the drive side and then sliding the whole lot back in.
Then I put on the non drive side bearing cage and tighten up the cone until there is zero play but no friction or bumpiness in the movement. I then hand tighten the locknut and check the movement again.
The next bit is the tricky bit. You have to hold the cone steady whilst you tighten the locknut against the cone so that the cone doesn't tighten by even a fraction of a turn (if it does, your bearings will be over tight). A decent cone spanner is a must for this job BTW.
As a guide, you should be able to rotate the axle between your thumb and forefinger with no effort and there should be no rough spots in the rotation.
I pop the wheel back on the bike, then I spin it and check for lateral play by trying to push the tyre from side to side. If it moves even a millimetre, I take the wheel off and try again.
Never be tempted to overtighten the bearings in the hope that they will wear in and run smooth. Wear will turn the grease into a grinding paste and shorten the life of your bearings.
I changed out my rear cup and cone axle six weeks ago and from memory, I reckon I had six attempts before I hit the "sweet spot".
I've clocked up over 700 miles since then and my rear wheel still runs like new.
It's worth the effort to get it right.