The short answer? Yes.

It's very possible that you could level up every crafting class you have without spending a single gil past what you make as you level, but the grind to do so is immeasurably longer than if you buy the materials for it. You'd essentially have to balance all of the crafting and gathering classes and level them all up at once. I'm sure one can find some sort of appeal to this method of leveling up the classes, but it's definitely easier, faster, and more economically sound to level up the classes by investing gil into materials.

You could also use the Ixal dailies to boost a crafting class about a level per day, and you can get a good amount of gil from the Ehcatl Sealants if you sell them on the marketplace. This is unfortunately limited to once per day though and isn't realistic if you're trying to get every crafting class to 50 within a reasonable amount of time.

Once you hit lv50 for each of the crafting and gathering classes though, it's a completely different story. You pretty much HAVE to invest money in materia and top gear in order to make anything that's worth selling anymore on the market place, and if you want to get gathering up to where you can get the latest materials you have to grind for gear in addition to buying the expensive sets.