Does activating delayed durability affect executing statements?
DELAYED_DURABILITY does not change the number of IO and CPU tick necessary to perform transactions in your server.  It can give a throughput boost to your workload, so you will expect to see the duration being reduced for the same transaction. Generally you expect to see an increase of Transactions/sec. This feature let transactions before being flushed to the transaction log file. 

In flight transactions will use the old setting and new transactions will use the new 'DELAYED_DURABILITY' setting.  I did confirm using #sqlhelp hashtag, Denny Cherry was kind enough to answer.

Be mindful that:


  You may still have log I/O contention if there is a high degree of
  concurrency, particularly if you fill up the log buffer faster than
  you flush it.


From Paul Randal's blog:


  Delayed durable transaction commits are asynchronous and report a
  commit as successful before the log records for the transaction are
  written to disk. Writing the transaction log entries to disk is
  required for a transaction to be durable. Delayed durable transactions
  become durable when the transaction log entries are flushed to disk.


From Books online:


  Delayed durable transaction commits are asynchronous and report a
  commit as successful before the log records for the transaction are
  written to disk. Writing the transaction log entries to disk is
  required for a transaction to be durable. Delayed durable transactions
  become durable when the transaction log entries are flushed to disk.


I suggest you also be totally aware of the risk of turning on this feature especially for all transactions as you did.  You have the capability of turning this feature on per transaction.

Few resource :


Control Transaction Durability
Paul Randal's post
Delayed durability performance by Aaron Bertrand