Fairly viable. The biggest things you miss out on not being able to get AC at all would be extra mags and inventory space. Additional mags only matter if you plan to play more than one "type" of class seriously (Which is to say if you main, say, Hunter and thus have an SATK mag, but also want to play as Ranger, Force or Braver it would be inconvenient not to have an RATK, TATK or DEX mag.) but it's not entirely necessary. Especially since alts get their own mag and you could make an alt to do so instead, and you can have up to 3 characters per account without paying for additional slots.
Inventory is a tight limit though. The basic inventory size without premium or any form of expansion is pretty small, and I highly recommend making alts if just to use their Character Storage as banks for things like stacks of 999 grinders and other items you don't strictly need, but don't want to throw out. Learning how to save inventory space becomes a very good skill when you're F2P.
More luxury things like a shop are compensated by FUN which you can get 3day shop passes with and stockpile for when you feel you need them. AC, and by extension features like premium, don't actually offer you that much in the way of objective gameplay advantages over other players as much as they offer a degree of convenience.