Are the phrases “at once” and “in one go” equally acceptable?

"At once" means immediately. I assume you mean "all at once". Yes, both all at once and in one go are acceptable and mean similar things, but they are different. "All at once" means simultaneously (so the described action must involve multiple objects), or else suddenly, while "in one go" means the object (not necessarily multiple) was accomplished in a single action (not necessarily suddenly).

Also, in one go is more British than American. Google Ngrams reports that the phrase comprises roughly 0.000027% of text in British English, but only 0.000006% in American English.