Not easily - Datasette is written in Python, so you could try running it in WebAssembly (like Mozilla did for Jupyter with https://hacks.mozilla.org/2019/03/iodide-an-experimental-too... ) but it would be enough work that it might be easier to reimplement a subset of Datasette directly in JavaScript.
I've got no experience with Datasette, but if it's all in pure python, then you can use Pyodide[0] to run it within a wasm module. I was surprised how easy it was - took about 15 minutes and I had a Python package working perfectly in the browser. The Python package is about 3x faster than the JS/wasm version, but I'm guessing that performance gap will narrow when we get wasm-gc.
