Can Exploratory Factor Analysis(EFA) be used if a questionnaire has already been developed with sets of items to measure particular constructs/latent variables?

In my opinion, when you have developed a questionnaire to measure a particular construct, you selected the items on the basis of some theoretical background. Therefore, you first can apply Confirmatory Factor Analysis (CFA) to check whether your theoretical assumption matches with empirical data. If you find your model is fit (or fits with minor correction on the basis of Modification Indices [MI] that commensurate theoretical basis) you need not to apply EFA. But if you find your CFA model is far from your expectations, you can apply EFA to identify existence of any sub factors in your questionnaire. Correct your model on the basis of EFA findings and theoretical supports and run CFA again. Ultimately you need to satisfy CFA for your questionnaire not EFA.