Yes. For many non-natives, they have to get over the meanings of "up", "in", and "out" before proceeding, and the predictable questions of how one signs "up" versus signs "in".
Sign up is required to join the website, sign in is required to access the website later, and sign out is the opposite of sign in.
That said these questions are always difficult because differing cultures/usages/dialects, even within one language, can dramatically affect comprehension. So a site really has to be tailored to the particular audience it seeks - a site in the US, the UK or India might use very different terms depending on the particular content it covers. But if you're targeting native speakers of English in most idioms I'm familiar with I think the terms above are pretty clear, and made clearer by using the same verb; other choices make them sound like unrelated actions, which they are not.
These composed verbs, whose meaning depend on the modifiers, are definitely confusing.
You can go a long way without mastering them, and their meaning (assuming there's only one) isn't always easy to infer from the roots. Think of getting off, for example.
Some of the combinations are still not part of my passive vocabulary[1], and most are not part of my active vocabulary, because I can usually get away with synonyms.
For this scenario, "log in" and "register" offer the best syntactic contrast, and should be favored, IMO. "Sign in" and "sign up" require more thinking. Pet peeve of mine, actually.
[1] There was a vocabulary depth study posted here on HN a while ago, I was at the 95th percentile of non-native speakers, equivalent to the median of natives of my age.
This group of customers may be larger than the group of native speakers depending on your target audience. So optimizing for non-native English speakers living in non-English speaking countries is something which should be considered.
... in English-speaking countries.
> [M]ost people would only have come across log in within a computer related context.
Most of the time, non-native speakers come across English in computer-related contexts, i.e. on the Web.
Getting particles (eg. "in" in "sign in") and prepositions right is one of the hardest parts of learning a new language. (Word gender for languages with that feature is another hard part.) You can understand almost everything of a website just from understanding verbs and nouns.