"I consider the government of the United States as interdicted by the Constitution from intermeddling in religious institutions, their doctrines, discipline, or exercises...Certainly, no power to prescribe any religious exercise or to assume authority in religious discipline has been delegated to the General Government...
"But it is only proposed that I should recommend, not prescribe a day of fasting and prayer. That is, that I should indirectly assume to the U.S. an authority over religious exercises which the Constitution has directly precluded them from.... I do not believe it is for the interest of religion to invite the civil magistrate to direct it's exercises, it's discipline, or it's doctrines; nor of the religious societies that the general government should be invested with the power of effecting any uniformity of time or matter among them. Fasting and prayer are religious exercises. The enjoining them an act of discipline. Every religious society has a right to determine for itself the times for these exercises, and the objects proper for them, according to their own particular tenets; and this right can never be safer than in their own hands, where the constitution has deposited it...every one must act according to the dictates of his own reason, and mine tells me that civil powers alone have been given to the President of the U.S. and no authority to direct the religious exercises of his constituents."
— -- Thomas Jefferson, to Samuel Miller, January 23, 1808
Probably
I strongly suspect he is running partly based on his rhetoric and behavior (both of which are that of a candidate) and partly based on some semi-inside info I have heard. As of 2 months ago he was definitely gearing up to run.
Having said that, he seems to have quieted down, if anything, since then. Either he wants to be a late entry or he is having second thoughts...or is getting offers. My bet is if he DOESN'T get in (and maybe even if he does) and if Hillary wins the nomination, Clark will be VP. I think it far less likely he will be VP if any of the other candidates get the nomination.
Interestingly, way back when I blogged all of this some months ago (you might want to look back at what is already blogged before asking), I mentioned that he would compete most with Hillary and, because of that, boost Obama. People didn't like my saying that! If you are correct in your analysis that he is aiming at Hillary, my analysis is probably correct.
Personally I am not a big fan of Clark. I think, like Hillary, he would make a perfectly good president, but he would not be my first choice.