Yes (at least there are cross-sectional correlations back up your intuition)
Bukowski et al. (2002) found a negative link. Their study was cited 39 times, pointing to more acceptance in the scientific community in comparison to the National Undergraduate Research Clearinghouse. You might want to go through the citing papers to find some information about the mechanism, the article is paywalled for me.
From their abstract:
The results showed that having a boyfriend/ girlfriend was related to poorer emotional and behavioral adjustment for those early adolescents who were unpopular among same-sex peers. For adolescents who were popular among same-sex peers, romantic involvement was not related to emotional and behavioral adjustment. Independently of same-sex peer acceptance, however, romantic involvement was negatively related to academic performance, albeit only for girls.
What does this say?
Well, it doesn't really give a hint for a causal relationship in either direction.
You can't (ethically and practically) do experimental random pairings of high school students, so the best we could hope for is natural experiments (looking at the time-lagged effects of getting in a relationship). Neyer & Asendorpf did that and found stable increases in conscientiousness and decreases in neuroticism (both of which could be good for academic performance). N&A had a student sample and they didn't assess academic performance, but I wanted to show an example of the research design, that would provide the best possible evidence.