First of all, there are many, many levels of belief, and often even a very low level can produce a lot of benefit, and make mitzvah observance worth something.
Secondly, in terms of negative commandments, the "Thou shalt nots," if a person refrains even for the wrong reasons, still he is refraining and not bringing all kinds of negative consequences onto himself and others.
In my experience a lack of belief is often related to a lack of a proper Jewish, Torah education. Without learning about our wonderful heritage it’s “difficult” to make an informed decision about belief. How can one believe or not believe something that one hasn’t tried to study and understand as much as possible?
If there is a basic belief in God, just a lack of understanding of the necessity of the mitzvah, then performance with trust in God that it is the right thing is really performance on a high level. The very acceptance of mitzvot by the Jewish people at Sinai was with the condition "Na'aseh v'nishma" ("We will do and we will understand"), meaning that we will do even before we understand.
True, a person should try to understand, and certainly an understanding of the background and fullness of the mitzvah will create a deepened satisfaction in mitzvah performance. This usually comes with increased Torah study. Lack of this understanding, however, does not take away from the fulfillment of the mitzvot.
