Is it possible to delete and append records to a table that takes part in a relationship with a feature class?
Of course! Provided you've got the required access to edit / add features to that table, you can most certainly work with it in the same way that you would any standalone table.
Now, as to whether the relate would actually work depends on how the relationship class is defined. A relationship may be 1:1, or it may be composite. The relate may be based on a field that you don't have available in the source dataset for appending, like a GUID / globalID. These things could make it harder or even impossible, but that can change based on the relationship class and the particular edit you want to make.