Yes. American Express gives the expected time-frame here:

http://www201.americanexpress.com/ge...wood-Preferred

Scroll down to the text that says,
"A complimentary upgrade to Starwood Gold

Enjoy an upgrade to Gold Preferred GuestŪ by spending $30,000 on the Card in a calendar year and earn StarpointsŪ even faster.

Then click on the numeral 13 to see:

If during any calendar year, Eligible Spending on your Card account is $30,000 or more, you (the Basic Cardmember) will be enrolled for at least twelve months in the Gold Preferred level of the Starwood Preferred GuestŪ loyalty program (unless you are already enrolled in an equivalent or higher level). Starwood associates excluded. Please allow 12-16 weeks after your Eligible Spending equals or exceeds such amount for the applicable year for enrollment to become effective.

Best regards,

William R. Sanders
Online Guest Feedback Coordinator
Starwood Hotels & Resorts Worldwide

[email protected]