Changing Support URL in iTunesConnect
Yes, you can change accompanying details of your app while waiting for review and after the review is complete.

Apple's documentation mentions the following, emphasis mine:


  iTunes Connect App Properties
  
  ...
  
  Many of the properties in the following sections are either locked or unlocked. Unlocked properties are always editable. Locked properties are only editable when your app is in an editable state. The tables in this section indicate whether a property is locked or unlocked. Changes you make to unlocked properties are posted immediately, but expect 24 hours for a full refresh of the change on the store.


Anecdotal stories suggest Apple do keep an eye on any changes you make but, as of now, no additional review is required.

Fields will be disabled and marked as Locked, if they can no longer be edited. Locked fields are deemed associated with a specific binary.