The short answer would appear to be “yes” – but not on a particular day of the prisoner’s own choosing.
In Florin Andrei v Romania  ECHR 400 the applicant, who had been detained for kidnapping, false imprisonment and extortion, complained about the conditions of the local prison cells in Constanţa and also alleged that while in detention in 2005, on the occasion of a religious festival on 15 August, he had asked to see a priest to make his confession but had received no response from the authorities.
Before the Third Section ECtHR he claimed, inter alia, that the physical conditions under which he had been held had violated his rights under Article 3 (inhuman and degrading treatment) and that the refusal to let him see a priest on 15 August 2005 had been in breach of Article 9 (thought, conscience and religion) ECHR. On the Article 9 issue, the Romanian Government countered that Andrei had not exhausted domestic remedies [para 51]. Alternatively, the Government claimed that it had been necessary for Andrei to be available on 15 August in order to be questioned by the prosecuting authorities along with his co-defendants and there had therefore been an objective reason for rejecting his request to see a priest. Moreover, Andrei had not repeated his request at any time during his subsequent detention [para 52].
The Court concluded that the physical conditions of Andrei’s detention had indeed violated Article 3 [para 48]. As to the alleged breach of Article 9, however, the Court had already found that Romania had a well-established regime of religious assistance for Orthodox Christians in places of detention: Iorgoiu v Romania  ECHR 1831/02. Given the circumstances, the fact that Andrei had not been able to make his confession on a specific day was not likely to prejudice his Article 9 rights and that aspect of his complaint was manifestly ill-founded.