[Rich Ives]

No - he cannot.

Per the Officia Baseball Rules used by pros and just about every youth organization in the country:

7.10 Any runner shall be called out, on appeal, when—
(a) After a fly ball is caught, he fails to retouch his original base before he or his original base is tagged;
Rule 7.10(a) Comment: “Retouch,” in this rule, means to tag up and start from a contact with the base after the ball is caught. A runner is not permitted to take a flying start from a position in back of his base.

For High Schoool Rules:

8-4 ART. 2 . . . Any runner is out when he:
o. positions himself behind a base to get a running start;