Generally, no, if you try to remove a Constituent that has an active Recurring Gift you will receive and error message that keeps you from completing the removal.  You can however remove a Constituent that has a Recurring Gift by using the Custom Constituent Import.  This has been identified as bug E-59901. Note that if you de-duped a constituent with a recurring gift, the recurring gift will be moved to the master record. Also if a constituent record is removed somehow in error, the recurring gift will continue to recur even though the constituent has been removed.