Maybe, but probably not. Postgrest still needs to talk to Postgres over the Postgres wire protocol, which isn't possible with wasm in the browser because there is no raw socket API. However, I'm sure there are some cool hacks you could do like running postgres-wasm "locally" (also within the browser) and having postgres talk to it. You'd still need to modify Postgrest to change how it speaks to Postgres, though.

This is also assuming you're running the WebAssembly in the browser. If you're running it in something like WASI, you might have access to a raw socket API and then maybe it's a different story.