Yes, but a lot of the things you'd be making are gear, which means you could put it in the Armory inventory for storage (as long as you didn't go fighting in it). The only one I'd expect to fill first is the weapon slot.
I guess that's true, but then when I want to go sell it I will have to move it back into the inventory anyways. All that extra work... lol
Hopefully the prices for selling to NPCs will get better at higher levels, but it still seems that there is not much incentive to sell anything before you get your retainer, and so your inventory may fill up.
Another inventory assist will be the grand company crafting turn-in's (can't remember proper title). It's not much, but soon enough we should know that items x, y & z from (e.g.) blacksmith show up repeatedly. So make a bunch of those to exp, store where able (armory/retainer/house etc), then trickle out to get exp + seals.
Not a huge assistance it's true, but once you've cleared a crafting log for a given level range, knowing what to craft to maximise effectiveness (increased exp gain for GC turns-ins, levequest turn-ins, components for higher-level recipes etc) will be very useful.
Yes, it doesn't help early on, but it's just more reason (imho) to smash a battle class to 20, to get GC/retainer/chocobo access ASAP. That's my plan, anyway.