I was looking thru my copy of the Constitution "Anatomy" book and saw what Corsair posted above. I was going to make a copy and comment, but........the book is in the basement and the scanner is upstairs. Also, I knew someone in the Group would do it, so it was just a matter of waiting.
But I will also chime in again. I have a printout of a monograph called, "Constitution, CLOSE UP: Minutiae For The Modeler and Artist by Commander Tyrone G. Martin, U.S. Navy (Retired) A Timonier Working Monograph February 2003 TGM" This pub is a wealth of minutia about the "Constitution". Any serious scale modeler of the "Constitution" should have a copy of this monograph. For example: concerning your question about the hoops, here are a couple of entries from the "Masts, Spars, Rigging, and Sails" Chapter:
"As completed in the spring of 1798, 'Constitution' was equipped with a bowsprit and three masts. Each was composed of several sections, each successive section of smaller diameter and length, and each section made from a single tree........'"
Thereafter follows contemporary data concerning various dimensions of the bowsprit and masts.
Then we have the following: "a listing of bowsprit dimensions noted in 1806 for the "Upper Tice[sic]; Lower Tice [sic]; Upper Side of Larboard fish; Upper side of upper fish) with the following paragraph, "This confirms the fact that the shift, noted in 1801 in "Constitution's" case, had been made from all pole masts to only the Mizzen being a pole mast......."
There are also excerpts from various contemporary sources listed. They appear to be from logs and letters and reports. Here are a couple pertaining to your question:
"14 July 1800 -- The new mainmast, a "made' mast, is to be 101' 6" tall"
"Aug 1801 -- Iron hoops were purchased for the fore and main masts and the bowsprit.
"11 Jun 1803 -- 'The main Mast.... is a made Mast consisting of 28 pieces"
So, the answer to your question is: It depends. It depends on what date or time span you want you model to represent. From launching to July 1801- no hoops; after 1801 (i.e. War of 1812)- hoops.