Answer
No — the Record Selector's displayed content is hardcoded at the framework/code level for standard LUs and can't be extended with additional detail through configuration. What IS configurable: existing items can be selectively hidden from the side selector panel (via its three-dot '...' menu), though this doesn't affect the separate dropdown-style selector's own content. For a Custom Page specifically (rather than a standard screen), there is a genuine configuration option: RMB on the custom form window's type > 'Update Record Selector', which lets you choose which element is actually displayed there.