Did Henry V’s archers at Agincourt fight with no pants / breeches on because of dysentery?

tl; dr

At least some of the archers who fought at the Battle of Agincourt almost were almost certainly suffering from dysentery contracted at Harfleur. However, most of the worst affected had been shipped home to England before Henry left Harfleur for Calais.

Is there any evidence in the chronicles of the time that some or most of the English & Welsh archers went into battle without breeches / pants / trousers?

Yes, there is good evidence from at least three chroniclers (Jean le Févre, Jehan de Waurin, and Enguerrand de Monstrelet). Le Févre and Waurin are of particular interest since they were both present at the battle. However, we cannot say whether these accounts were written wholly independently, or whether there was an element of copying.

Would archers with dysentery have had the strength to draw their longbows and fight if they had so little control over their bodily functions that they had to remove clothing from the lower regions?

The result of the battle suggests that the answer is an emphatic "yes".

Evidence for Dysentery in Henry's Army at Agincourt

There is certainly good evidence from the chronicles that some in the English army were suffering from dysentery contracted at Harfleur. For example, Thomas Walsingham's Chronica Maiora

"When the king of England had settled matters at Harfleur as befitted a king and a victor, he decided to proceed by land towards Calais with quite a small force, not more, so it is said, than eight thousand archers and armed men, a great many of whom were hampered by the dysentery they had picked up at Harfleur ..."

However, we should be careful not to overestimate the numbers. We have (incomplete) lists of those infected with the 'bloody flux' (dysentery) who were sent back to England from Harfleur. Professor Anne Curry has analysed the data, and has proposed that the majority of those in Henry's army that were infected with dysentery had been sent back to England before he departed Harfleur on his march to Calais.

Juliet Barker's quote

The quote from Juliet Barker's Agincourt: The King, the Campaign, the Battle (published in the US as Agincourt : Henry V and the battle that made England) is:

Many of the archers were reduced to cutting off their soiled breeches and undergarments in an attempt to allow nature to take its course more easily — an option not available to the men-at-arms, encased in their padded steel plate armour. Grim though the sight of them must have been, the smell was probably worse.

The sources that Juliet Barker cites for this are:

• Le Févre: Jean le Févre, Chronique de Jean le Févre, Seigneur de St Remy, ed. by François Morand (Société de l’Histoire de France, Paris, 1876-81), 2 vols. (vol i, pp 252-3),
• Bacquet: Azincourt, 1977, p 93

Le Féver was a contemporary chronicler.

The Chronicles

Le Févre states:

"Lesquelz archiers estoient, la plus grant partie, sans armeures en leurs pourpoins, leurs chausses avallées, ayans haches et congnies pendans à leurs chaintures, ou longes espées; les aucuns tous nudz piez, et les aucuns portoient hunettes ou cappelines de cuyr bouilly, et les aucuns d'ozières sur lesquelz avoit une croisure de fer."

Le Févre is one of three particularly important contemporary sources for the battle which were written in France. The other two are La chronique d'Enguerran de Monstrelet, by Enguerrand de Monstrelet (available to read or download as pdf files from archive.org) and Recueil des croniques et anchiennes istories de la Grant Bretaigne, à présent nommé Engleterre by Jehan de Waurin (also available to read or download as pdf files from archive.org).

Le Févre and Waurin are considered to be particularly valuable since both men took part in the battle (le Févre with the English, and Waurin on the French side).

These three chronicles agree very closely. However, whether this means that they provide independent corroboration for other, or that the overlap is evidence of copying remains a matter for scholarly debate.

These questions are addressed by Anne Curry in her book The Battle of Agincourt: Sources and Interpretations (pp 135-)

Professor Curry has combined the evidence from these three chronicles on this point, and translated them thus:

Most of these archers were without armour, dressed in their doublets, their hose loose round their knees, having axes or swords hanging from their belts

• Curry, Anne: The Battle of Agincourt: Sources and Interpretations, p 160 (my emphasis)

Yet another chronicle, the Chronique de Ruisseauville describes the English army in the early stages of the battle thus:

"They came very quickly, the archers in front running without armour and with their breeches hanging down, always firing on the French ..."

• Quoted in Curry, Anne: The Battle of Agincourt: Sources and Interpretations, p 125 (my emphasis)

Now, exactly how many of the archers actually fought with 'their hose loose around their knees', or 'their breeches hanging down' is something we will probably never know. But some in Henry's army were undoubtedly suffering from dysentery during the battle, and the chroniclers are explicit that some, at least, dropped their hose before they fought. It seems reasonable that these facts are related.

As to your last question:

Would archers with dysentery have had the strength to draw their longbows and fight if they had so little control over their bodily functions that they had to remove clothing from the lower regions?

I would say that adrenaline is a wonderful thing, and that (up to) twenty thousand Frenchmen charging towards you probably helped provide motivation.

More seriously, these were men who had trained their whole lives with the longbow. Even in their weakened state they would have been able to employ it to devastating effect.

Which is exactly what the contemporary chronicles say they did during the battle.