Report - Patches Needed by Multiple Computers

Yes, in fact, there are several datasources in the WSUS Analytics report category that contain group membership information.

The datasources Approved Updates Installation Summary Info By Group, Approved Updates Installation Summary Info With Approval Details, and Computer Update Status With Approval Information contain a field that provides a row for each applicable update and computer for each group that the computer belongs to. The field is called Computer Group or Computer Group Name. To filter on this field, use an EQUALS operator and specify the desired group name.

Also the datasources Computer Update Status with Computer Information, Computer Update Status With Details and Computer Update Status with Approval Information contain a field named Group Memberships, which is a delimited list of all group memberships for that computer. To filter on this field, use a CONTAINS operator and specify the desired group name.

The easiest way to get there is to start with the Computer Update Status system report. Modify it to use the desired alternate datasource, add the group field from the alternate datasource, and filter on group names(s).