The command doesn't know. That's why you need to check the SQLCODE variable.

If SQLCODE  = 0 then the row exists and it was updated. If SQLCODE  = 100 then the row doesn't exist. If it not equal to either then you have a problem.

Example for Embedded SQL:

 &SQL(update WH.Size
   set Height = 1000
 where %ID = 10)
 write SQLCODE

Example for Dynamic SQL:

 SET myquery = "update WH.Size set Height = 1000 where %ID = 10"
 SET tStatement = ##class(%SQL.Statement).%New()
 SET tStatus = tStatement.%Prepare(myquery)
 SET rset = tStatement.%Execute()
 write rset.%SQLCODE

Not sure what you mean by "if the row exists" in regards with insert. The row does not exist, because you're creating it.

Yep, that was my first thought - can you change Property Organizations As list Of Organization; to parent/children Relationship? In this case you will get automatic cascade delete. You'll have

Relationship Responce As GetOrgUpdatesResponse  [ Cardinality = parent, Inverse = Organizations ];
Relationship Organizations As Organization [ Cardinality = children, Inverse = Responce ];

And it suggests that each responce has its own organizations objects that don't repeat.

Otherwise, you will have to delete them manually 1 by 1 in callback method %OnDelete for example

/// This callback method is invoked by the <METHOD>%Delete</METHOD> method to 
/// provide notification that the object specified by <VAR>oid</VAR> is being deleted.
/// If this method returns an error then the object will not be deleted.
ClassMethod %OnDelete(oid As %ObjectIdentity) As %Status [ Private, ServerOnly = 1 ]
	Quit $$$OK