I don't believe so. However, if a Mastodon user @s a Lemmy community like @music@beehaw.org in their post, it should get posted to that community, too. If Lemmy gets big enough then maybe Mastodon accounts will start adding tags like that alongside regular hashtags.

Boost, no. Since there's no quote boost. If you @ mention the community in your toot, it will create a post in the community.