rd: The State doesn’t provide citizenships to geirum from the Bnei Brak beis din (an issue that is irrelevant to the OP) but the Rabbanut most certainly does recognize the validity of their conversions.
What other sense could you think Rav Elyashev meant it, other than halachic, when he specifically stated that someone who underwent a geirus all the while believing the world to be older than 6000 years, that the conversion was never valid and he remains a gentile?