Yes, that's why he could have been a good 'military clown', he wasn't very ambitious and had core values.
One of which was a hate of the Directorate and, AFAIK, an absence of the useful political connections. Which means that (a) he would not be looked upon as a suitable ‘clown’ by the politicians (as he was not in OTL) and (b) he would not be able or willing to carry a coup as a purely military affair.
I also think that with Napoleon dead ITTL, Moreau could be pragmatic and try a coup with Sieyès.
Taking into an account that there were no, AFAIK, indications of anything of the kind before Bonaparte returned, this belongs to a category “possible because does not violate the laws of physics” 😉
I just checked out and that's true that Moreau was getting increasingly unpopular both among the people and the elites. Joubert still dead ITTL, it would left Bernadotte. The problem is that Sieyès hated him and was convinced he was preparing a coup without him. He also lacked other important supports and if his influence within the army was good, it wasn't enough to make a coup on its own. It was still possible, but he needed Time, so maybe we could have seen Bernadotte's coup take place in 1801-1802, after the end of the 2nd Coalition and when the Directoire would still be more in trouble. In this case, Bernadotte would become a dicator, but less autocratic than Napoleon, and by keeping the Republic, I Guess, even if monarchy didn't bother him that much After all (mmh Sweden).
If anything, Bernadotte at that time had a better chance than Moreau because he had connections both political (not on the very top but nonetgeless) and military. But he was still a convinced republican and not an adventurous type. He would lead
if asked officially (IIRC Nappy made a comment to that effect, but maybe somebody else) or arrest the plotters
if ordered but that’s it. However, if ending up on the top, he would most probably disappoint Sieyes even if not in a manner Nappy did.
As for the timing, after the failed attempt of the assassination in 1800 Nappy commented that “Bernadotte would play Anthony”. He was commander of the Army of the West stationed in Vendee, Councilor of the State and both Joseph and Lucien Bonaparte had been in prominent positions. In his farewell note to Bernadotte on his way to Italy, Napoleon wrote: "I am going to fling myself once more into the hazards of war. We do not know how it may turn out. If I fall, you will find yourself with 40,000 men at the gates of Paris. In your hands will be the fate of the Republic." What was going by default, was that Bernadotte will take care of the Bonaparte family.