No. Approval voting is actually a minimized score voting system, and although intuitively a two-point feels like this should convey less information, the way the aggregation rule works (straight addition—or specifically in the approval voting case, tallying), you're actually extracting significantly more information out of a set of approval votes than you would from a ranked choice vote.
To put it another way: given a (sufficiently large) set of [0,1] score votes, you can generate a set of approval votes that give a very good estimate for the score voting results by mapping each score vote to an approval vote by randomly picking a number in [0,1) for each vote and marking options scored above that threshold. Handwaving a bit, this implies that at scale approval voting and arbitrary-precision score voting give the same results with pretty good probability.
Now, score voting with arbitrary precision pretty clearly conveys more information than ranked choice! You can extract an RCV from a score vote directly, but this loses substantial information about how far apart the options were rated. Conversely, if you extract a score vote from an RCV, you ... well, you can get something like Borda count. For other RCV aggregation algorithms a score vote extraction is not quite as clean, but it's substantially less clear whether the information "lost" is real or an accidental artifact of the RCV itself. Certainly you can argue all day over the merits of Borda count and variants vs other IRV aggregation algorithms, but then score voting with arbitrary precision not only strictly dominates Borda count, but also is clearly conveying additional information about degree of preference on top of that which is obviously useful and not encoded in ranked choice votes at all!
Bonus: a surprisingly large number of decisions are dominated by no more than three viable choices that are clearly preferred over all others. When selecting for among three options, there are seven unique approval votes (the all marked/unmarked votes, expressing no preference, are equivalent), and only six ranked unique choice votes. It should be pretty clear that RCV and approval don't convey equivalent information in this case!
In a nutshell, the reason this works is because the people who approve only X or Y have a pretty similar X versus Y opinion as the whole electorate, just based on random chance. It's just statistical sampling principles.
> When selecting for among three options, there are seven unique approval votes (the all marked/unmarked votes, expressing no preference, are equivalent), and only six ranked unique choice votes.
No, they're both six. There are 8 unique approval votes (2^3) but two are thrown out -- the all-marked and all-unmarked, so you're left with 6, same as ranked. RCV and approval absolutely do convey equivalent information in the case of three candidates.
No they do not convey equivalent information, because the information content isn't just the number of states, it's the encoding mechanism too.
For instance suppose you encode the position of missile strikes on some land area in a 16x16 grid, meaning 8 bits of information.
Another person uses only six bits of information, encoding the missile strike position as degrees and distance from the center point of the grid.
Then it turns out the latter method is more accurate because the missiles tend to always strike pretty close to the center of the grid.
The specific patterns of voter preference that emerge in a realistic scenario are counterintuitive and can end up being more accurately measured by the kind of expression approval voting allows. You can get people who have radically different intensity of preference but the same order of preference so that they look identical to a ranked voting method but appear different to approval voting based on their thresholds.
In addition, you have tactical behavior, as well as the efficiency of how the voting method uses the information on the ballots. When you combine all of these factors together, approval voting tends to perform better than ranked voting methods.
It's a pretty interesting topic on which a common intuition (n bits is less information content than log(n!), right?) fails it turns out most of the work is being done in the aggregation algorithm, not in the data entry.
Which is emblematic of the biggest problem with RCV, which is that the aggregation algorithms are too opaque to realize at a glance that the results they give are ... not as good as doing a straightforward thing.
So the strength of RCV would then be more built in tie-breaking.