Hello InternetB,
there are additional mechanisms like ebgp fast-external fallover that tears down the eBGP session as soon as the link to the eBGP peer is detected down.
Even without this when BGP holdtime expires the session is torned down and learned routes are removed.
You don't need to use clear ip bgp * to get this.
link failure Detection time is link dependent and it can take up to 3 keepalives (30 seconds).
ebgp fast external fall-over is enabled by default in modern IOS images.
Hope to help
Giuseppe