Can You Receive Friend Requests While Offline on Xbox Live? No

No. Friend requests are delivered via Xbox Live servers. If you're offline / disconnected / signed out, the request cannot reach your profile.

What Happens

• Sender sees "Request sent."
• You see nothing until you sign in to Xbox Live.
• Upon sign-in, pending requests appear in notifications / Friends & clubs.

Related

• Appear Offline: You're still connected—requests arrive, but you're shown as offline to others.
• Xbox 360 vs. Xbox One/Series: Same behavior—Live connectivity required.

To receive requests, stay signed in (even if "Appear Offline").