Well, you won't be able to do ranked.
You will be harassed at every menu telling you subscribers gain benefits.
Everything will cost more credits and you will be able to store fewer credits. In this sense, it might be a pain to buy augments.
I think you have to buy with CC some cosmetic options like hide helmet and color unification.
If you want to level a new character from scratch, your play experience will be pretty frustrating.
Overall, it is doable, but quite limiting and frankly, frustrating to play without being a sub. There are probably many things I'm missing that are annoying that others will pick up.