Say my character, a fourth level Sorcerer, takes a level into Wizard on level 5- this would grant the first third level spell slots this character could use. Given this, does this mean the character, if they had the material resources, could copy spells of first through third level into the spellbook?
No this is not the case. From the multiclassing rules in chapter 6:
Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.
As a wizard, you can only copy spells you can prepare, not necessarily for which you have spell slots.
Copying a Spell into the Book. When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare.
So even having a 3rd level spell slot does not allow you to prepare those spells, however you could cast a spell as a 3rd level spell (such as magic missile
Say my character, a fourth level Sorcerer, takes a level into Wizard on level 5- this would grant the first third level spell slots this character could use. Given this, does this mean the character, if they had the material resources, could copy spells of first through third level into the spellbook?
No this is not the case. From the multiclassing rules in chapter 6:
As a wizard, you can only copy spells you can prepare, not necessarily for which you have spell slots.
So even having a 3rd level spell slot does not allow you to prepare those spells, however you could cast a spell as a 3rd level spell (such as magic missile
Subclass: Dwarven Defender - Dragonborn Paragon
Feats: Artificer Apprentice
Monsters: Sheep - Spellbreaker Warforged Titan
Magic Items: Whipier - Ring of Secret Storage - Collar of the Guardian
Monster template: Skeletal Creature