No, you can't combine time in the UK on Tier 2 and on
Exempt status.
Appendix Skilled Worker of the UK Immigration Rules wrote:Qualifying period requirement for settlement as a Skilled Worker
SW 21.1. The applicant must have spent a continuous period of 5 years in the UK.
SW 21.2. The 5-year continuous period must consist of time with permission on any of, or any combination of, the following routes:
(a) Skilled Worker; or
(b) Global talent; or
(c) Innovator; or
(d) T2 Minister of Religion; or
(e) T2 Sportsperson; or
(f) Representative of an Overseas Business; or
(g) as a Tier 1 Migrant, other than as a Tier 1 (Graduate Entrepreneur) Migrant.
Even if you switch back to the Skilled Worker category, your ILR clock will reset to zero as the requirement is a
continuous residence of five years in the UK under the specific categories listed above.
Generally the only way to acquire ILR by a combination of categories is on the 10 year Long Residence route.
By definition, people exempt from the Immigration Rules, by for example working for an international organisation, do not have any pathway to ILR under the Immigration Rules, as they are exempt from those very Rules that grant ILR. By contrast, any continuous legal residence in the UK counts towards Long Residence.
EDIT: I am no longer sure if people on Exempt status are even eligible for ILR under Long Residence. The last paragraph of the
Exempt page on the gov.uk site states "It is not possible to apply the provisions of the Immigration Rules to people who are not subject to UK legislation.".
If people with Exempt status are not subject to UK legislation at all, by definition, they can't acquire ILR, which is a status under UK legislation, at all.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.