Are the OVA of "Baka and Test" more closely related to the manga/light novels than the anime's first season?
Yes
The OVA, titled Baka to Test to Shoukanjuu: Matsuri (Matsuri = festival), is based on the school festival episode in the 2nd volume of the original source, which is the light novel. (Source: Japanese Wikipedia)

OVA
[...] 原作2巻を元にした学園祭のエピソード。 [...]


Additional info: Japanese Wikipedia also mentions that the story development between the original source and anime's 1st season is different, and even included a lot of anime original story. The 2nd season continues the 1st season's setting while also adapting the original source more faithfully.

特徴

第1期は原作とは異なるストーリー展開、及びアニメオリジナルの展開が多い。第2期は第1期の設定を引き継ぎつつも、原作を忠実に再現している。 [...]