The answer is yes.
Pleasure implies sensations, which not always bring happiness.
Even a licit pleasure can be an ambush that devours him who gives himself over to it beyond a reasonable measure. When examining the relationship between happiness and pleasure, Saint Thomas Aquinas quotes Boetius: “He who decides to look back on the excesses of his past will notice that such pleasures have a sad end.” 
Pleasure, therefore, is like salt: it needs to be used with moderation.
Divine Providence, kind and maternal, allows the great majority of men to have at least some happiness in this life, though causing those It loves the most to go through periods in which happiness disappears completely.
Those are the great periods in one’s life. Later, night falls and happiness disappears. Even supernatural consolation disappears. One enters the dark tunnel of a great unhappiness. But in general, critical or acute evils do not last. And so one goes on living.
A different way is that of happiness without pleasure. There are phases in the history of certain peoples and civilizations in which pleasure is so exceptional and entertainment so rare that it is as if they did not exist. There are two or three feasts per year, of any kind, and outside of that people do not have fun. Can a person be happy in these conditions?
He certainly can, as long as he understands the situation and figures how to find in it the happiness that it can yield. This is what we could call happiness in one’s situation.
8. An example: a Brazilian farmer at the time of the Empire
Let us consider the life of a Brazilian farmer at the time of the Empire. How did he live? How did his family live?
Since at that time there was no automobile, this man had a tendency to isolate himself in his family and lead a placid life there.
There were usually two or three feasts per year. There was the Novena of the Patron Saint of the parish in the neighboring city. In those days the farmer would go to town with his whole family.
He was also the patriarch, that is, the man around whom life on the farm revolved. He was the natural leader. If farm workers had a problem, it was he who would help them solve it.
In that small place he had one of the pleasures life can give man: the happiness of being honored, respected and considered to a degree appropriate to his function.
The old farmer was an example of happiness without pleasure, yet true happiness, however unlikely that might seem nowadays.
 De Consolatione Philosophiae, apud Saint Thomas, Summa Theologica I-II, q. 2, a. 6, sed contra.