Apparently not.
// 01.js
console.log('01.js Hello world');
console.log(`01.js uid: ${process.getuid()}`);
console.log(`01.js euid: ${process.geteuid()}`);
db.getSiblingDB('foo').bar.createIndex({lastUpdated:1});
$ docker compose logs | grep 01.js
mongo-0-a-1 | /usr/local/bin/docker-entrypoint.sh: running /docker-entrypoint-initdb.d/01.js
mongo-0-a-1 | 01.js Hello world
mongo-0-a-1 | 01.js uid: 999
mongo-0-a-1 | 01.js euid: 999