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Yes, the function $f^{1/n}$ converges to $2^{-1/2}e^{-1/4}=0.5507$ for large $n$: $$f^{1/n}=\prod_{j\ne i}|\lambda_i-\lambda_j|^{1/n} =\exp\left(n^{-1}\sum_{i\neq j}\ln|\lambda_i-\lambda_j|\right)$$ $$\qquad\rightarrow\exp\left(\int \rho(\lambda)d\lambda\int \rho(\mu)d\mu\,\ln|\lambda-\mu|\right)=\exp\left(-\tfrac{1}{4} -\tfrac{1}{2}\ln 2\right),$$ with $\rho(\lambda)$ the eigenvalue density in the large-$n$ limit (Wigner semicircle), given by $$\rho(\lambda)=\frac{1}{\pi}\sqrt{2-\lambda^2},\;\;\lambda\in(-\sqrt 2,\sqrt 2).$$