There is very little evidence that would indicate exactly how common using bracers was for medieval archers. Not only are we lacking in detailed accounts of archery techniques and practices from medieval Europe, bracers would probably be personal equipment (like daggers or shooting gloves) and would not be likely to show up in armory inventories.

However, there are a few textual references to draw on. In the General Prologue of Chaucer's Canterbury Tales, the equipment of the Knight's Yeoman is described in detail and "Upon his arm he baar a gay bracer." Although Chaucer was likely no archer himself, he participated in English wars and would have come into contact with plenty of military archers. As the Yeoman of the prologue is intended to be an archetypical example of the English retinue archer, we can at least say that bracers would not be uncommon.

Another source, Roger Ascham's Toxophilus, is the first English manual of the bow and was written in 1545 (so slightly after the heyday of the longbow). Ascham has this to say of the bracer:

ittle is to be said of the bracer. A bracer[2] serveth for two causes, one to save his arm from the stripe of the string, and his doublet from wearing; and the other is, that the string gliding sharply and quickly off the bracer, may make the sharper shot. For if the string should light upon the bare sleeve, the strength of the shoot should stop and die there. But it is best, by my judgement, to give the bow so much bent, that the string need never touch a man's arm, and so should a man need no bracer, as I know many good archers which occupy none. In a bracer a man must take heed of three things ; that it have no nails in it, that it have no buckles, that it be fast on with laces without agglets. For the nails will sheer in sunder a man's string before he be ware, and so put his bow in jeopardy : buckles and agglets at unwares shall raze his bow, a thing both evil for the sight, and perilous for fretting. And thus a bracer is only had for this purpose, that the string may have ready passage.

So he suggests that both bracers and no bracers were common practices. However, if an archer did not use a bracer, this would be because they were shooting in such a way that the string had no contact with the arm. If the string doesn't touch the arm, it would be impossible for them to build up a callus. Actually, I don't even know if it's physically possible to develop a callus against a full-size warbow. I don't know the biology behind calluses, but I think the slap of the string on your arm would just skin you rather than toughen you up.