Could we use randomizedsearchcv during nested cross validation?
You can. Just be aware that in every iteration of the outer loop of the cross-validation, a different set of hyperparameters will be evaluated, meaning that the generalization performance (the score computed in the outer loop) does not correspond to a given set of parameters, but rather a set of optimized models.
This is similar to what we do in the Regularization of linear regression model notebook where a set of equally valid alphas are found for RidgeCV.
Also take into account that the computational cost increases with the number of iterations of the RandomizedSearchCV (which should itself be increased when adding hyperparameters), so cross-validating those results will increase the required computing resources as many times as folds you evaluate.