https://github.com/osquery/osquery/pull/6910 would this cause any problems for Fleet?

I don't anticipate problems. Fleet has supported TLS 1.2 and 1.3 for years.

Would Fleet also be able to deprecate 1.0 and 1.1 in a similar fashion?

Yeah, actually funny enough this came up today. https://osquery.slack.com/archives/C01DXJL16D8/p1611149960030400 tl;dr Fleet already disables them by default and with the 3.7.0 release support for those will be removed entirely.