Let me start by saying that I'm a RuneScape veteran so you can kind of see where I'm coming from.
So, one of the things I really loved about RS is that it really let you take your own path. You weren't just restricted to combat. You want to fishing/woodcutting/cooking/mining/smithing/framing Tree Of Savior gold? Go ahead, albeit these skills are a lot more useless than they were many years ago but that's another story.
My point being, is it possible that we'll see different kind of progression paths for secondary skills? So let's say woodcutting for example, you could go from novice woodcutter-->lumberjack--> wood muncher. And I don't mean woodcutting just for woodcutting's sake. I mean having all the produce from those skills be intrinsically woven into the game.
Eg: Certain logs from certain trees are used in a potion made by Botany to be able to fight a certain monster.
Creating demand for those skills basically and not just have them be something on the side.
I know there is the alchemist class which is a good step in the right direction in my opinion. I would very much like to see more like it.
A: Becoming a Alchemist/Squire/Pardoner doesn't give you any profession related work to do. Basically it means you can buy ingredients from NPC and start up AFK shop for services/crafting. You don't really farm for materials either.
I don't think ToS will have any in depht profession system if that you are asking, than just growing plants and pets in guild area.
B: On topic though, is it possible? Not in the way you described, but otherwise sure. You won't progress in classes from a squire to blacksmith or something like in your example of woodcutters, but you can keep taking squire to obtain new skills or improve the effects of your craft; in this case weapon and armor maintenance.
Aside from that, it seems that this is a suggestion of what you'd like to see from the game. It's probably best to share that on the forums where it might be read by someone who can affect the game.
C: I'll submit the idea of the Gambling professions Sorcerer and Necromancer, through the /cardbattle system.
At a glance, it looks like a 50/50, but if you can predict what card your opponent might toss out, you can throw out a card with significantly higher odds at winning the spin.
Since Cards are only really useful to Sorcerer and Necromancer(at time of writing) for leveling their summons, it's a neat mostly-worthless currency to gamble with.
Granted, it doesn't have the "become the guy who makes a quest line possible" sort of artisanship you mentioned, but It is a "skill" you can level up through experience that benefits your job.