Should an update statement query plan ever go parallel?

Question

If an update statement's query plan does go parallel, does it guarantee a communication buffer resource deadlock, or is that determined by whether the parallel plan is using all cores?

Answer 1

From the documentation:

The update and delete operators in a parallel query execution plan are executed serially, but the WHERE clause of an UPDATE or a DELETE statement may be executed in parallel. The actual data changes are then serially applied to the database.

As to your second question,

does it guarantee a communication buffer resource deadlock

Any deadlock is predicated on the query / queries being run and how they are structured and executed, SQL Server does not inherently guarantee any deadlocks on its own.