If a job applicant has suffered from a debilitating illness in the past, can they be excluded from the shortlist?

No, not for that reason alone. Where someone has had an illness in the past that at the time would have amounted to a disability under the Equality Act 2010, it will be discriminatory to reject the person for employment for this reason (s.6(4) of the Equality Act 2010). A history of cancer or depressive illness would be good examples.