I am not sure about the deeper research, but there are reasons to expect using fingers to be connected to numbers.
Research on young children (e.g. 3 days old) show that they also do simple number comparisons (1, 2 and 3) in areas of the brain where we also do eye-hand coordination and problem solving. Young adults continue to use these same brain regions for certain work (estimation) with numbers. (Something similar also shows up in experiments with animals .. so this is a broadly based biological association.)
When we see how many cultures also use fingers for counting and early math, and the ways in which we use 'balance' (of weights and hands, etc.) to understand equations, the fingers are part of how math is done. This is but one of several ways in which we do math. So learners need to develop several different skills and to connect them. Multiple representations, multiple skills, multiple approaches are the model for the most effective problem solvers in mathematics.