Anecdotal evidence: As a child, I was bilingual in English and Polish. Learning Polish (from my maternal grandmother, AKA Babcia) took a minimal amount of time from my exposure to English.
But it did have a strong influence on acquiring vocabulary items by semantic associations, not by spelling associations. It also gave me more sensitivity to learning roots and constructions in other languages.
One deficiency: I never had much interest in word games that depend on spelling, such as Scrabble, cross-word puzzles, etc.
That might be a research topic: For speakers with comparable vocabulary size, what is the effect of bilingualism on speed in solving crossword puzzles?
John