NTS is initialized using a relatively expensive, but short lived, TCP TLS session. NTP loss due to rate limiting will require more frequent TCP initializations.
The NTP size-blocks I've observed have been hard, not rate limits. Martin Langer provided a table showing sizes between 228 and 1468 bytes depending on the encryption algorithm and number of cookies. I've asked the NTS authors about potential workarounds, but suspect it would be difficult. The authors have also confirmed that size blocks have been detected during NTS tests.
The secure time transfer of NTS was designed to avoid amplification attacks. Impairment of UDP port 123 could require use of alternate UDP port(s), which might be unpopular.