To reassure u Jed, on a technical level it will work, since any plant will grow when given light, water, air & food. But the thing u have to appreciate is that that same technical level is a very wide spectrum and goes all the way from minimal supplying of needs resulting in small, weak, barely alive plants, all the way up to perfectly supplying maximum levels of its various needs resulting in super heavy crops. With ur set-up, at a nutshell guess, i'd say that if u considered my technical spectrum to be a 10 stage system then ur set-up would probably rank around level 3.
BUt dont get too tied up on the full technical side of the equipment - learn the biology & stages of the plant growing more as it is this that will give u better results if ur starting out. Any equipment will grow something but u wanna concentrate more on making sure it comes out strong & healthy by harvest, rather than worrying about size of everything. There's no point spending loads on top equipment if u dunno how the plant grows or what its doing - u'll just waste money & good equipment won't correct mistakes for u any better than cheap equipment will. Grow something small, cheap & cheerful now so when u do step up on equipment in the future, u'll know how to use it to max out ur growing.