Yeah, I feel that for zerg it's pretty much sweet because half the time I don't scout til I have lings anyway (yayy overlords ^.^) and always FE. Terran is in the middle because they have so many openers, many of which are quite flexible and allow you to transition smoothly into what you wanted to do in the first place. I think toss definitely have it the hardest against random as stated in Pinder's post. Perhaps you have to rely on your superior knowledge on a matchup/crisper timings to win and in that way I think they do have an advantage.
On the flipside, if you disregard cheese I don't feel like it's a huge advantage because I highly doubt that they are going to be executing each build for each race and matchup perfectly (or close to perfect). Perhaps they will be a little ahead, say, if they got a much earlier expansion that you couldn't punish. But this shouldn't be game-ending in anyway. You can possibly try throwing them a curve ball and doing a weird build or uncommon strat yourself to play off their disadvantage of having to know all 9 match ups as there's no way they can know how to effectively with every situation.
If you lose to a random player only because you didn't know what race they were at the beginning it's up to you not to take too much from it. It's not like you're playing random players every second match (or at least I hope not o_O) and in a lot of tournaments they make you choose a single race anyway.
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