I've seen the drill manuals for muskets, but did these new professional armies also drill raw recruits in sword use?
What kind of non-gunpowder training regimen would they have had other than pikes?
The Swedish Carolean army drilled in sword practice.
The Värja m/1685 (rapier model 1685) was a standard side-arm for both pikemen and musketeers. 340 000 were made from 1686 to 1737.
The swords were forged out of high quality steel, and each blade was tested by the tip being put between the upper end of a door and a door post and a man suspending his entire weight on the hilt - the blade was supposed to bend, but not crack or deform, and spring back into shape after being released. The blade was then sharpened and a feather released from head height. The blade had to be sharp enough to cut the feather in two mid-air to be approved.
The Carolean infantry was drilled to march double-quick at the enemy. The battalion consisted of 600 men, 150 men wide and 4 men deep, with each rank consisting of 50 pikemen in the centre and 50 musketeers on either flank. The musketeers were to release a volley at 70 and 20 paces - with no reloading. The first two ranks fired at 70 paces and the second two passed them and marched to 20 paces and fired. After that, the battalion would charge with pike and bayonet (not all troops had bayonets as the Great Nordic War started in 1700 and would draw their rapiers instead). As long as formation could be kept, the troops were to use bayonets and pikes, but if the enemy started to run and formation broke down, the pikemen were to lay down their pikes and the musketeers to hand their muskets on their shoulders and draw swords.
The troops were drilled to thrust their rapiers towards the upper body of the enemy solders - if they were armed (with a cuirass, for example) they were to aim for the eyes. Fencing was not drilled - troops were supposed to deliver 3-4 rapid thrusts on an enemy, take him and advance on the next man, not engage in fencing. If an enemy stood with a bayonet mounted on his musket, the Carolean was supposed to use his own bayonet (and bayonet fencing was drilled to some extent) or his pike, with which had much longer range than the musket-mounted bayonet of his enemy.
At Helsingborg 1710, the Swedish pikemen "tumbled over" several Danish infantry formations that tried to stand with bayonet and musket, causing the Danes to re-introduce the pike with their troops in order to be able to stand against such charges in the future.
What probably happened is that the front ranks of the Danish formation either got killed, wounded or came in disorder trying to avoid the pikes and the rear ranks, taking a few steps back at the carnage met the pikemen with swords out and started routing. To the Danish commander, it might have looked like his infantry, which stood without retreating, facing the initial charge (which is a feat of high morale and discipline), was simply destroyed by the Swedish charge, which looked like it did not even slow down as it destroyed the Danish formation.
Speaking on the Spanish armies, by the 1600s the sword was not considered a main weapon anymore, rather as a backup weapon for pikeman and musketeers/arquebusiers alike.
All that said, the Spanish model was that soldiers had to drill and (ideally) they would have a few years' training in garrisons before they are considered ready for the front lines. The best training ground was Italy. There, soldiers are expected to drill with their fellow soldiers, led by the sergeant major who was responsible to teaching the soldiers on formations, maneuver, offense, and defense.
The focus on musket/arquebus drills reflect both the difficulty in maintaining fire rate and reliability, and the rising importance of firearms.