That's an interesting question. After Obama won, there were campaigns in Latin America running (and winning) under the slogan "Si Se Puede", yes we can. So it is definitely true that an American president can influence the region without even trying (or knowing it).
My feeling is the opposite, though. Latin America has the kind of "strong man" government. For centuries, the leader has been a strong person, who can enforce his will. Chavez and Castro fit perfectly this role: the primary difference they hope to portray is that they are exercising their strength to help the people (rather than the rich and themselves). And actually, all the very popular presidents in Latin America that I can think of portrayed themselves as using their strength to help the common people.
So, will Trump be push people to the left, or to the right? I think we can agree that Trump will be perceived as a strong man (whether he actually is or not, that's irrelevant). So part of it will be how he pushes his wall deal, and immigration, and trade deals. Will people in latin america realize he is just trying to help Americans? Will they feel like he gave them a fair deal? Will they feel he respects them? Those are the kinds of questions to answer.
The other side of the coin is in Latin America itself. The wave seems to be going against leftism (that's such a stupid fuzzy term), with Argentina swinging right, and with Brazil swinging right, and Venezuela falling to pieces. A lot of the wave that rose during the Bush administration was pushed by Venezuela, supported with their oil money.
So in the end, while Trump would have some influence on the region if he became president, everything will be viewed from the lens of local politics, and the trends already happening in the region will be the primary determiners.
btw Ecuador has kind of an unusual relationship with the US because it uses US dollars. I was in El Salvador when they switched to dollars, and it completely drove the leftists insane.