Can Galley post alerts in Slack, Teams or Google Chat?

Yes, with the chat alerts add-on, on any plan. Galley posts to the channels you choose in Slack, Microsoft Teams or Google Chat, and each post links back to the page in Galley (Open in Galley). Each channel gets the alerts you tick:

An investor opens the data room
An investor opens a document
An investor downloads a document
An investor accepts their invitation
An investor accepts the NDA
An investor asks a question
An investor asks for a document
Someone asks for access to the data room
An investor shows strong interest (the same signs as hot investors)

So a channel isn't flooded:

An investor's visit is one post a day, a few minutes after they arrive, listing the documents they opened by then. Later visits that day aren't posted.
Documents downloaded together, such as a folder as a ZIP, are one post.
A channel gets at most 10 posts a minute. Any more go as one post saying how many, with a link to Activity.

Without the add-on, Company settings (click your picture at the top right, then Company settings) says so under Chat alerts, with Add chat alerts, which opens your 1936 AI account.