yes, that is a perfectly viable approach, i wanted to do that same thing this year but i couldn't, the mainboard i want is a bit too expensive and it limits me to ddr3 and a fm2 cpu, but my budget is very limited atm
this is my situation and i think you had in mind that same idea
i build a itx pc for basic stuff, be pretty on a itx case, be silent, play some games, be cheap and last for some years
all well on that plan, 8 gbs ddr3, a itx mainboard, a ssd, a 1 tb hard disk, and a small am1 cpu
all perfect, but i decided to use it to play gta v, so add a gpu, it worked, but the am1 is slow for this game, so upgrade rignt?
cpu on tht mainboard can't be really upgraded, there is noe abit faster but is not that faster to help at all
next step is get anew itx mainboard, a fm2 cpu and reuse the ram, right?
couldn't find a mainboard and while i tried to find the mainboard i spent the money for the cpu on other stuff, so the am1 stays in place
now that the am4 socket came, the r5 will come in june and a itx mainboard will come, but is ddr4, so the idea of reuse parts i had vanished
more or less what you would face if you decide to go with the fx, but the intel could let you skip most of those problems thanks to ddr4 and a possible couple more cpus worth to buy and use on the mainbard you buy
then we return to the fanboy stuff and the fx not recommendable option, and the intel offering more atm in your case with your budget