Nope. All group message events that are published to relays have no personally identifiable metadata attached to them. Only a random 32-byte group_id value (that can change over time, groups can also use multiple group_id values if they want). The content field of these events is an encrypted payload which, once decrypted, is itself is an encrypted payload that contains the actual group message. These events are published using one-time nostr identities each time.

If you're in the group, you know where to look for the group's messages and how to decrypt them. If you're not, all you can see is a relative amount of activity for a given group_id value (at least until it changes).