I think, this will not work as the public will not the reach it (not even search it).
Ok, let assume you have domain example.com which is registered and on registrar level and it has has NS records pointing to ns1.xxx.ovh.com - this information is propagated to DNS zone for .com domain to establish delegation for the domain site.com.
There would be working DNS server with configured zone example.com on the server ns1.xxx.ovh.com. Once anybody would query some record it iterates from "root" to ns1.xxx.ovh.com which is authoritative server for this domain and this server know or don't know...
NS record for the zone directly is more important in upper level then in level of domain itself and it doesn't cause "next server" to query...
If you want to have records for site2 and site3 subdomain to be managed in AWS you need to delegate directly subdomain on ns1.xxx.ovh.com.
site2.example.com. 3600 IN NS ns111.awsdns-xz.co.
site2.example.com. 3600 IN NS ns112.awsdns-xz.co.
site2.example.com. 3600 IN NS ns113.awsdns-xz.co.
site3.example.com. 3600 IN NS ns111.awsdns-xz.co.
site3.example.com. 3600 IN NS ns112.awsdns-xz.co.
site3.example.com. 3600 IN NS ns113.awsdns-xz.co.
then once the the query will come to ns1.xxx.ovh.com it will delegate query to AWS DNS system so these records will be handled outside of ns1.xxx.ovh.com. This delegation cover mentioned domain and its sub domains so site2.example.com NS will cover site2.site.com and also www.site2.example.com for the delegation.
The result would looks like (in case of TTL 3600):
@ 3600 IN A <IP>
@ 3600 IN MX 10 mx.example.com.
@ 3600 IN NS ns1.xxx.ovh.com.
sub 3600 IN A <IP>
mx 3600 IN A <IP>
site2.example.com. 3600 IN NS ns111.awsdns-xz.co.
site2.example.com. 3600 IN NS ns112.awsdns-xz.co.
site2.example.com. 3600 IN NS ns113.awsdns-xz.co.
site3.example.com. 3600 IN NS ns111.awsdns-xz.co.
site3.example.com. 3600 IN NS ns112.awsdns-xz.co.
site3.example.com. 3600 IN NS ns113.awsdns-xz.co.
-- edit --
Added NS record for @ and also priority for MX records to have it in valid form and consistent.