That's internal conflict, and it makes the world go round.
More specifically, it adds drama to your work.
And now my patented Unforgiven/Casablanca lecture:
I've done this one before, but here goes. I like to think of "Unforgiven" and "Casablanca" as two movies that do an excellent job of showing varieties of internal vs. external conflict--and "want" vs. "need."
In both of these movies, a main character is faced with a (morally ambiguous) choice between what's *right* and what's *desirable.*
In Casablanca, Bogart eventually has to choose between throwing his rival for a woman's love to the wolves (Nazis) or allowing his lover to escape to America with her freedom-fighter husband while returning to a war he abandoned. Bogart's character *was* a freedom fighter as well, and he lost that part of himself--in the course of the movie, he reclaims his honor and his purpose, and loses the woman he loves. But a larger task--fighting the Nazis--is carried on on two fronts. He gives up what he wants--his lover--and gets what he needs--himself.
In Unforgiven, a retired gunfighter goes back for one last shot at the money (which he needs to raise his children). This is, to me, a more morally ambiguous movie--but the upshot of it is that Eastwood's character, while he accomplishes good in the course of the movie (killing a brutal sheriff, saving a young man who thinks he wants to be a gunfighter from himself, helping a brutalized young woman reclaim her life) -- at the end of the movie, Eastwood's character *loses* himself. He loses the peace he's claimed, the distance from the brutal man he used to be, and is forced to accept that he is, in the final analysis, a monster. He gets what he wants--revenge, safety for his children--and loses what he needs--his soul.
That's internal conflict: the tension between things you want and need, or (even better) two things that you need and can't have both of.
External conflict drives the overt story, but the internal conflict is what makes the story resonate for readers beyond the point of eye candy.
On to the actual question: Yes, conflict is essential to engage the reader. Ideally, that conflict should begin with the first sentence on the first page, and that sentence should also in some way indicate something about the questions the story or novel is going to address. That conflict can be in the reader rather than the characters--two classic examples of conflict-created-in-the-reader are le Guin's "The Ones Who Walk Away from Omelas" and Clarke's "The Nine Billion Names of God."
Our own Charlie Finlay's "Footnotes" is another great example of this. These are commonly known as "idea stories" and are usually brief and are very, very, very difficult to do well.
A story in its simplest analysis (and this isn't all stories, just most of them) boils down to character in situation with problem. You need to establish that problem from the beginning of the first page.
In a novel length work, you have a little more leeway in introducing the primary conflict, but you must establish *A* conflict and a stake very quickly or your readers--won't. Read, that is.
(Caveat--slice of life literary pieces, but really does anybody actually READ those? Or do they just teach classes on them?)