Assuming you mean VMWare HA, no, distributed switching is not a requirement, however having at least two datastores is, to enable datastore heartbeating. In terms of your question, "Live Migration" is a specific capability of vmotion - notably it is not the feature used to manage VM availability if a host goes down.
However, by my reading of their compatibility page, you are not running a supported combination - for all releases of vSphere 6.7, ONTAP 9.3 is the minimum version, while for the FAS2240-2, ONTAP 9.1 is the maximum version. vSphere 6.5 U3 will support whatever you're running on the FAS2240 however.
It's a standards compliant communication protocol, so it should work, but in the end it is up to VMWare if they choose to support it, and they do not.