Kind of? But not really. It's more like a series of "rock/paper/scissors" as opposed to a broad rock/paper/scissors.
For example, Sword characters. They all have fundamentally the same different strengths and weaknesses. Long range, above average power, typically have good jabs, somewhat slow frame data, usually poorer recovery options, usually not-so-rewarding throws, etc. So you can go like "Oh okay. Let's just label them as 'scissors' and call it a day."
However, it doesn't work that way. Not all sword characters have projectiles like Toon/Link (or tether grabs for that matter), some sword characters have far more explosive power than others (Ike/Marth/Roy), some have more range than others (Corrin/Shulk), some have a completely unique mechanic that makes them stand out from the entire cast (Cloud/Shulk), and some don't REALLY fit into the conventions of being a typical Sword character at all (Meta Knight). And then you have Pit/Dark Pit, whom are just plain weird.
Something that would be more accurate would be like "Marth is Scissors/Scissors/Paper, while Ike is Scissors/Rock/Rock". It sounds redundant, I know, but it works better because it more accurately represents the amount of options and potential matchup spreads more accurately than a sweeping broad term. But it's even far more dynamic than that, because both players and stages can also widely affect matchups and go beyond just the character's own innate set of tools. It's also important to factor in how the tools are being used, how effectively that they are being used, and also when and where they are being used that yields the most effective results when presented with any number of unique situations.
In short: Paper/Rock/Scissors can never fully convey the complete depth and complexity of fighting games, and especially the characters within them. You can somewhat use them to briefly describe how a character's options interact with another character's options, like the common phrase "Attack > Grab > Shield > Attack", but not even this accurately depicts the actions that are being performed within the game by either the players or the characters. Because as a quick example, some grabs (Pac-Man's) are way worse and less threatening than other grabs (DK/Bowser/The Marios/etc).