No - the spirits must be aged in the oak. Buying wine that has been stored in oak means only that you paying someone else to store something you will still have to store for an additional two years,. I'm not competent to comment on whether distilling wine that has been in oak will benefit the brandy produced.
Stipping out the excess verbiage to get to the basic, we get, "In the case of brandy distilled from wine of grapes, which has been stored in oak containers for less than 2 years, the statement of class and type shall be immediately preceded, in the same size and kind of type, by the word “immature”.
So, I see your logic. Does the phrase "which has been stored in oak containers for less than two years," modify "brandy" or modify "wine of grape." The answer to that lies in the age statement, in §5.40, again simplified for clarity, and referring only to grape brandy, not other fruit brandy:
(b) Statements of age for brandy, Age may, but need not, be stated on labels of brandies, except that an appropriate statement with respect to age shall appear on the brand label in case of brandy (other than immature brandies which are not customarily stored in oak containers) not stored in oak containers for a period of at least 2 years." And age means, by the definition at 5.11, "The period during which, after distillation and before bottling, distilled spirits have been stored in oak containers.