A new review study by Amez and Baert examined the existing research on the use of smartphones and the consequences for academic success.

In short:

• A predominance of empirical results supporting a negative association.
• This finding is driven by studies relying on actual GPA measures.

But, there is one important limitation:

• The literature’s main limitation is that its results cannot be causally interpreted.

And the researchers go even a bit further in the conclusion:

In this article, we reviewed the scientific literature to date on the relationship between smartphone use and academic performance in tertiary education. Our analysis of the literature reveals a predominance of empirical results supporting a negative association. However, this predominance is less outspoken in studies analysing data gathered by paper and pen questionnaires (compared with studies on data gathered by online surveys) and studies relying on self-reported grade point averages (compared with studies using actual grades). In general, when scholars use methods of data gathering which are more susceptible to social desirable behaviour, a non-significant association is found more often.

Abstract of the study:

We present the first systematic review of the scientific literature on smartphone use and academic success. We synthesise the theoretical mechanisms, empirical approaches, and empirical findings described in the multidisciplinary literature to date. Our analysis of the literature reveals a predominance of empirical results supporting a negative association between students’ frequency of smartphone use and their academic success. However, the strength of this association is heterogeneous by (a) the method of data gathering, (b) the measures of academic performance used in the analysis, and (c) the measures of smartphone use adopted. The main limitation identified in the literature is that the reported associations cannot be given a causal interpretation. Based on the reviewed findings and limitations, directions for further research are discussed.