So there are a couple of aspects to this question:

Technically speaking, you're broadly right: mail would offer at least some protection against an 18th century bayonet. It probably wouldn't be quite as useful as on a medieval battlefield, simply because muskets are really heavy and so can hit really hard in a thrust - a Brown Bess weighs around 5kg, while a halberd might weigh around 3kg and a spear more like 2kg. But mail can be pretty good armour, so it would probably still turn aside some thrusts.

However, a bayonet thrust is one of the rarest potential injuries a soldier would face in an 18th century battle. Artillery fire would cause the lion's share of casualties, followed by small arms fire. Only a fraction of engagements closed to cold steel, and even if they did a musket is just as useful as a club. So for the vast majority of your casualties, wearing a mail shirt would give them no extra protection. Indeed, providing another source of rusty metal fragments that might end up driven into wounds potentially could have increased the risk to a soldier should they get shot, which would easily outweigh any slight benefit in a bayonet fight. And it's important to remember that armour is heavy, so your soldiers might be likely to throw it away - even if they are wearing it, the impact on their fatigue over a day of fighting might well be enough to outweigh any benefit in a close quarters engagement.

Beyond that, making mail is a pain. To produce useful armour, the links need to be closed by riveting or welding, not just bent into shape (which is the normal method used today in 'mail armour' intended for costume/display/re-enactment purposes). This would have been a very time consuming process. When 18th century armies did use armour (in a limited capacity for cavalry) they turned to plate cuirasses instead of mail shirts, which offer better protection and would have been easier to manufacture with the level of industrialisation available.

To sum up: it would provide protection against bayonets, but that small advantage is not enough to outweigh the cost and practicality of outfitting infantry soldiers with mail armour on a large scale in 18th century European warfare.