First off: The patch will
not lead to deflation, it will lead to inflation instead. But that has nothing whatsoever to do with professions.
Price is determined by supply and demand. That includes supply of gold, too. If everyone is swimming in gold then prices rise, if gold is hard to come by they drop. The patch introduced higher gold rewards from garrison missions through a follower trait so the overall gold generated will rise which means prices on average will rise.
Professions don't have a role in that at all since profession items can not be bought or sold for (a meaningful amount of) gold to NPCs. Gold is not generated or lost when trading a profession item, it is only re-distributed. By changing the re-distribution of profession items in the auction house prices for individual items will shift but as a whole they will neither increase nor decrease.
What will most likely happen is that basic resources get more expensive (more ways to spend them) while items made from time gated resources and bloods become cheaper (more ways to create them). The combination of both (the overall price of the "average" basket of trade goods consumed by the player base) will get slightly more expensive because of the increased overall gold in the economy.
This is a rather shitty change because it means that farming (which is toxic gameplay) and with that also botting become way more attractive than they already are. Using time gated resources and making farmed ones almost useless was an awesome move from Blizzard and could have been a first step to get rid of the toxic farming stuff completely (e.g. making all resources time gated instead of farmable) and I'm very sad to see them going in the opposite direction now.
Theoretically the patch could still lead to deflation, though. If people decide to farm more basic materials the supply will increase. If that supply increases faster than the supply of gold then prices will drop. But let's be realistic here: Most basic mats are generated by bots, simply because they can farm all day long. It's bad but it's the reality. They are running anyway, no matter the mat price on the auction house. The supply increase from players starting to farm more will probably be negligible.
This is a real issue but I think it's less severe than you think. There are not many people with 12 max lvl toons. Most players don't even have 3. And those won't all be running missions on a daily basis. The general player base is way less active than you might think
The overall effect of this is real but I wouldn't call it "mass producing" a currency. In the end it's not worse than people farming daily quests which gave significant gold rewards.
Auction house fees also counter balance that. Gold increase in the economy is fixed by the amount Blizzard gives us via the garrision, vendor prices or quest rewards. Gold decrease in the economy is determined mainly by auction house fees (plus maybe cost for repairs, those add up and are paid by everyone). If prices rise then the auction house fees (calculated as percentage of the price) rise, too, until there is a balance between gold generation and gold destruction. It's a self-regulating system and a mild inflation should be able to raise the average auction house fee high enough to counter the additional gold influx from treasure hunters.