Did Grenadiers use "Grenades" in the Napoleonic Wars

No, they didn't. Except possibly in exceptionally rare circumstances.

The following is adapted and expanded from an earlier answer of mine:

The soldiers which, by the time of the Napoleonic wars, were known as "grenadiers" did indeed start out as throwers of hand grenades. In most major armies who had them, specialised units dedicated to this task were established in the 16- and early 1700s. Grenades at the time were hollow iron balls, filled with gunpowder and lit with a fuse (think a Donald Duck/cartoon-style bomb, and you should get the picture). The contraption was fairly heavy, and throwing it accurately from distance required training and strength. Nor were grenades particularly useful on the open battlefield. As weapons they were from the very beginning really intended for use in assaults upon confined or fortified positions.

Storming prepared or entrenched positions, such as wall breaches or fortified buildings, were extremely hazardous operations for the individual infantryman, and required significant physical and mental exertion. Height, posture, and overall body build was also thought to contribute to the psychological aspect of warfare. Who wants to get into a close fight with someone much bigger than you? For all of the above reasons, grenadier units from very early on therefore began being purposefully composed of the strongest, tallest individuals available. As a consequence of being picked troops, they also got a reputation for being stronger/more elite than other infantrymen.

Unfortunately - or fortunately, as it may be - by the middle of the 18th century, the hand grenade had largely lost its place in the regular infantry arsenal. The reasons for this are multifold. They were very specialised weapons to begin with, and so had limited utility. In fact, it's unlikely that even the very early iterations of grenadiers were routinely armed with grenades. At least I've not found any reference to such in Danish-Norwegian sources. The grenades were kept as unit-level ammunition, to be issued when the situation demanded it. Hand grenades had also been made obsolete by improvements in arms. Lighter, more precise artillery pieces could now do much of the job which grenades had previously been expected to do - and could do it better. The grenade was retained into the 19th century for use in specific circumstances (such as ship boarding actions), but would not find more widespread use again before the First World War and the advent of trench warfare brought about a major revival.

Grenadiers in western armies gradually stopped being equipped with grenades from the early-1700s onwards. Thus the period when grenadiers actually threw grenades was short indeed. Yet soldiers known as “grenadiers” were retained, largely because their difficult task of dedicated assault troops remained, and because of their acquired status as elite units made up of strong and well trained men. Many period armies also reinforced this image by maintaining stricter height requirements for grenadier recruits, as well as issuing them with better/more elaborate equipment symbolic of their status. Grenadier units would often retain their high caps, mitres/bearskins or similar, originally issued in lieu of the wider tricorns commonly used by other infantrymen, slow-match cases, swords and other pieces of dress or equipment, left over from an earlier age. This view of grenadiers being the army’s elite soldiers would also spread from the line infantry to other branches. Thus you have various cases of grenadier-cavalry, grenadier-jaegers and suchlike turning up in the late 1700s/early 1800s.

By the latter half of the 1700s grenadiers had become firmly established as the elite shock troops of western armies. They were bigger and taller than other infantrymen, and they had more elaborate equipment, including tall caps (which made them look bigger and more imposing still). Many units would also allow, or even require the growth of elaborate moustaches or facial hair in order to build up an image of manliness or ferocity. On the battlefield they would operate as ordinary line infantry, yet they were also still often expected to act as professional storm troops, leading bayonet charges or assaulting breaches in fortifications. If operating in line alongside other line troops, grenadier units would commonly be placed at the right end of the line, as that was considered the most prestigious place.

When it comes to organisation and tactical doctrine, there is a lot of variation between countries and armies. Few nations operated dedicated grenadier regiments, although they did exist. More commonly, line regiments or battalions would have a grenadier company in addition to 4-10 “ordinary” companies. Such companies could operate as an elite part of the line unit as a whole, or they could be detached and/or combined with other detached grenadier companies in order to form a dedicated unit for specialised work or just a strong reserve.

All of this is good in theory. Yet in practice, by the early years of the 19th century, many western armies were finding that specialised shock troops were rarely worth the effort. Ordinary line infantry were expected to charge/fight with bayonets when required. Reserving the bravest/most imposing men for grenadier work was taking these men away from other units where they could be used.

There are also a range of military innovations taking place towards the end of the 18th and into the beginnings of the 19th century, which impact the usefulness of operating grenadiers in their traditional role. Firstly, development (both technically and tactically) of more flexible artillery units, meant that concentrations of heavy fire could much more quickly and reliably be brought to bear on enemy weak points. As a result, cannon became much more capable of preparing the way for a close assault, reducing the need for dedicated storm troops. The same can be said of the increasing use of the column of attack rather than line (often referred to as l’ordre profond replacing l’ordre mince). The column emphasised shock, rather than firepower, and allowed a large body of relatively less trained men to concentrate offensive power in a close assault – again reducing the need for traditional grenadier assaults. Finally, the gradual move towards more flexible operations, relying on mobility and adaptability reduced the reliance on traditional army organisation. In 1775 the French General Pierre de Bourcet for the first time proposed that armies operate in separate divisions, each capable of carrying out sustained all-arms actions independently of each other. This had been made possible by the growing reliability and power of both infantry weapons, such as the flint-lock musket with ring bayonet, and artillery. Many of these technical developments had taken place in the early 18th century, but it took a long time for most contemporaries to recognise the implications of individual soldiers or smaller units being able much more reliably to hold their own against larger formations. These developments in turn increased the importance of flexible light infantry, as against the more rigid and disciplined line formations of the preceding centuries. Thus, traditional grenadier “shock” units were increasingly becoming a remnant of 18th century professionalism, in an age of more flexible mass warfare. They were still an elite, but the practical/tactical benefits of operating grenadiers as opposed to ordinary line infantry were diminishing.

Some countries would abolish grenadier units altogether – Norway being one of the first, in 1810 replacing grenadier companies with jaeger/light infantry companies – while many other places they gradually became indistinguishable from other line infantry units. By the mid-1800s, the grenadier title was largely honorific, although even today the term many places retains an air of elite status or professionalism.

Sources

(most of these are in Danish or Norwegian, but I’m sure there are many other redditors who can contribute relevant reading in other languages)

Holm, Terje; Med plotons! Høire-sving! Marsch! Marsch!: Norsk taktikk og stridsteknikk på begynnelsen av 1800-tallet, med hovedvekt lagt på fotfolket; Forsvarsmuseets småskrift nr 7; Oslo, 1991
Howard, Michael; War in European History; Opus, 1976
Ottosen, Morten Nordhagen og Glenthøj, Rasmus (red.); Samfunn i krig: Norden 1808-09; Unipub, 2012
Petersen, Karsten Skjold; Kongens klæder: Hærens uniformer og udrustning i Danmark-Norge; Gads Forlag, 2015
Wilmar, Erik Dag; Hvor forberedt var den norske hær på krig i 1814?: Med fokus på organisasjon, utrustning og ledelse; MA thesis, University of Oslo; Oslo, 2001

edit: fixed typos