About three or four months later, babies begin to suck their hands or fingers, basically because they begin to know how to put their hands to their mouths (no, they are not teeth) and because, as you well know, with suction they calm down a lot.
This hobby can be quite constant in some babies, especially if they have never used the pacifier, and sometimes they can replace some milk with the simple fact that with the finger they can calm down, delaying hunger for later. The question to solve then is: Can the finger make our baby eat less? Logically, this question also works by changing "finger" to "pacifier."
The answer, as I said above, is yes. Breast milk (and artificial milk too) is given on demand and, as we have explained on other occasions, crying is a late sign of hunger. This means that when a toddler is awake and starts to open and close his mouth, sometimes even trying to put his hands to his mouth, he is hungry.
If at that time we put the pacifier and begins to suck until he falls asleep runs out of taking the shot he was waiting for. If this happens once a day, it is not a major problem, because it will compensate for what you have not eaten in successive shots. However, if this happens every time you want to eat, or several times, there may be weight problems because you are not eating enough.
Now, we are talking about children of 3 or 4 months who, in theory, already eat what they want and need and who have taken a fondness for the finger. It can happen that in some shot, as with the pacifier of the little ones, they calm down or sleep before having eaten. Perhaps throughout the day they end up compensating for what they have not eaten as they do those children who suck less because their mothers simply lengthen the time between the shots, or perhaps yes, from so much "eating" the finger they end up eating something less.
This doesn't have to be worrisome, especially since most children put their fingers in their mouths and because surely they have always done it (our parents, grandparents, great-grandparents and so on you go to know what homo sapiens). If the child grows and fattens at a normal pace, he will be eating enough.
If instead he is not gaining the necessary weight and we really see an association between the finger and the lack of food: "since he sleeps with the finger he is eating much less," it could be interesting try to make him eat more, offering his chest more often (and see what happens, maybe he is losing weight for another cause). The truth is that speaking of babies with the ability to ask without problems when they are hungry, it's strange that problems occur derivatives of the pacifier or the finger in the mouth.
