Yes. There is a subset of patients with depression who have either of two different genetic polymorphisms for methyeneltetrahydrofolate reductase. This may be causally linked to their depression. [1]
Supplementing diet with a modified form of folate appears to diminish depression in patients with these particular polymorphisms.
My understanding is that this is still a matter of controversy.
1) Prevalence of MTHFR gene variants you refer to is very high, e.g. 10%/50% for homo/heterozygous C677T SNP [1] (with frequencies varying substantially between ethnic groups).
2) Effects tend to be stronger with two copies of a variant (homozygous), but a single copy (heterozygous) may still be a concern, e.g. for C677T: "Individuals with the 677TT genotype, have approximately 30% the MTHFR enzyme activity of those with the 677CC genotype, whereas heterozygotes 677CT have around 65% of enzymatic activity" [2]
3) It seems odd to me that pharmacological dosages of folate are getting prescribed (I mean, it's a nutrient so why take it in doses that exceed the nutritional range?):
"The most active form of folate has recently been approved in the United States as a prescription medical food for depressed patients with folate deficiency. Doses are usually 7.5 to 15 mg/d". [3]
"Another concern is that folate doses > 800 μg/d can result in high levels of unmetabolized serum folic acid, reducing
the amount of brain l-methylfolate and leading to decreased monoamines, an outcome that potentially increases the risk
of or exacerbates depression." [3]
Folate RDA is 400-800 μg/d depending on pregnancy status [4]
Supplementing diet with a modified form of folate appears to diminish depression in patients with these particular polymorphisms.
My understanding is that this is still a matter of controversy.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1810582/