There's a recent publication out that goes into the mechanics of this and these issues.  I haven't read a lot of this book yet (just got it) but there are two separate things you are asking, related yes but each have different effects. 
The book is called "Ammunition Demystified" by Jeff Siewert

FWIW, I have experimented with chambers cut to match a brand/size of case - to my opinionated theory - yes, the headspace made a difference in ideal conditions.  Shooting in the conditions I generally find myself in though, it was insignificant - one of those one or two percent effect items.
My 2¢
 
Hoping to hear more thoughts... 

The answer is a definitive YES, it matters.

However, as some have pointed out, the errors may easily be eclipsed by other factors, so as to not affect the final outcome significantly for most shooters.

The definitive factors that headspace as you describe it affects in accuracy are:
1)  Alignment of the bullet into the leade/throat
2)  Initial non-axial movement of the bullet
3)  Fit of the bullet into the bore.

on 1:  If the chamber is sized to center the cartridge correctly, the bullet is aligned with the bore perfectly.  If the chamber is oversize, having it fall back slightly from the end of the chamber can cause mis-alignment.  

on 2:  As the powder charge goes off, the bullet inertia is greater than the case inertia because of higher weight.  The case therefore moves backwards; this can cause non-axial forces to be placed on the bullet by the moving brass, particularly as the pressure hasn't built enough to expand the brass fully to the chamber.  The brass may also expand non-uniformly, adding to the non-axial forces exerted by the brass onto the bullet. The case head not square to the breechblock puts considerable side force on the case also. 

on 3:  If headspace is excessive, and the cartridge is held back by the bullet jammed into the lands, there is a short ring of unsupported bullet between the brass end and the throat.  The bullet can bump up into this space, and then get swaged down into the leade/throat/barrel.  This deformation of the bullet can make it less accurate.

All this is theoretical, the actual effect on the accuracy can be unmeasurable, or significant, depending on the severity of the unstabilizing forces applied to the bullet by each factor.

To answer your question directly:  I have found that seating the bullets out to jam into the rifling will improve accuracy with .45 cal lead bullets.  

I have also found that buying my brass and dies and mold to match my barrel, and then specifying a reamer that matches all those components so as to eliminate all three factors above, along with careful chambering, makes .45 cal lead bullets a lot more accurate.  

So my answer is that, in MY experience, minimizing headspace and chamber length and chamber diameter issues, along with good workmanship is the single biggest factor in achieving good accuracy.   

I also believe that given no control over the chamber (existing rifle), jamming the bullet into the rifling is the best work-around you can do to improve accuracy.

Old-Win wrote on Apr 18^th, 2023 at 1:50pm:

Now that I have a way to increase the rim thickness of my cases I have done so on some test cases and will try them out soon. I have pretty much done the other accuracy tweaks that were mentioned, or one can think of to do, and while my accuracy is very good right now I want to see if I can improve it further or perhaps rid myself of the occasional flyers. 
While at silhouette matches I do get the occasional flyer that I scratch my head wondering if it was me or some unseen condition change.

I know that A. W. Peterson used to chamber his 22 rimfire Ballards so that the breechblock put pressure on the head of the case.

Center fire reloaded cases. If the case is not resized, ex Lee Collet Die or breech seat, then after 1 or 2 firings the case head-breech block clearance is ~ 0 and stays 0.
Accuracy is unaffected by "headspace" if case is not sized. See breech seating results.

It ain't the case head-breech block clearance; it's the fire-resize-fire cycle that damages cases and accuracy when headspace is excessive.

Rim thickness means nothing after the first shot. Fire, extract case, cut off the rim, reprime, powder, breech seat, fire, extract with rod -repeat.

My Winchester Helm rifle in 32-40 Krag has excess headspace. It doesn't seem to make any difference in accuracy. At a match last August I was behind after the first day so I had to shoot some really great targets on the second day to catch up. After deciding to resort to using a scope in the any sight match, the first five shots on my last target were less than stellar so I took a break, went back to center, gave myself a pep talk and really bore down for the last five shots of the match. My last five shots were two 25s, two 24s and a 23. Score was 212-2c. A decent target but not good enough to catch up and finished fourth.  The excess headspace played no part in my poor performance.   

Premod70 wrote on Apr 19^th, 2023 at 4:23pm:


  I can relate to that all to well, always thought it was just focus.  A new wording for an old excuse.