You are correct, Thompson's announcement coincidently was scheduled just after the September 5th debate.
He has said he'll take part in some of them, but frankly, there are not that many people watching them, so he'll likely reach more people in his visits directly to the Republican voters.
FNC New Hampshire debate: Ratings…
Last night’s New Hampshire Republican debate on FNC was the most watched debate of the 2007 election season. 3.1 million viewers tuned in; 854,000 in the 25-54 Demo. FNC’s debate last night beat all of ABC’s, CNN’s and MSNBC’s previous debates this year based on Total Viewers. The above numbers are Live but the Live+SD numbers are even higher.
FDT is speaking in FL to crowds in the hundreds, no more than three per day. If Thompson had appeared at the debate the ratings would have even higher. And he could have appeared on Leno the next evening to double up. But it takes effort, talent and skill to perform in a debate, the lack of which provides the best explanation for Fred's no-show.