The text does not give any indication as to whether or when Shylock fulfills the injunctions put upon him by the Court regarding converting to Christianity. We can only infer whether he does convert or not. There are two parts to his sentence. The Duke by law was obliged to convict Shylock to death for plotting against Antonio's life:

That indirectly and directly too
Thou hast contrived against the very life
Of the defendant; (Portia IV.i)

The Duke, in order to teach Shylock Christian mercy, pardons Shylock's life but sentences him regarding his wealth: half his wealth is to go to Antonio and the other half into the Duke's (the state's) own coffers as a fine. Antonio intercedes and relinquishes the half appointed to him requesting only that he have use of Shylock's wealth during Shylock's lifetime and that Lorenzo receive it upon Shylock's death. Antonio adds that Shylock must convert to Christianity.

ANTONIO
    [...]
    Two things provided more, that, for this favour,
    He presently become a Christian;
    The other, that he do record a gift,
    Here in the court, of all he dies possess'd,
    Unto his son Lorenzo and his daughter.
DUKE
    He shall do this, or else I do recant
    The pardon that I late pronounced here.
[...]
SHYLOCK
    I am content.
PORTIA
    Clerk, draw a deed of gift.
SHYLOCK
    I pray you, give me leave to go from hence;
    I am not well: send the deed after me,
    And I will sign it.
DUKE
    Get thee gone, but do it.
[...]
    Exit SHYLOCK (IV.i)

We know that Shylock says to send the contracts about the gift over to his house and he will sign them. We can be confident that this is what happens. We know that regarding the conversion the Duke says, "Get thee gone, but do it." We know that many Jews were forced to convert to Christianity and faced terrible punishments, including confiscation of goods and expulsion from the country, for practicing Jewish ritual after a forced conversion. We know that the Duke expects obedience since he can "recant / The pardon that [he] late pronounced." We seem to hear a slight doubt of follow-through in the Duke's last words: "but do it."

We do not know for sure, but from all these textual and cultural factors that we do know, we can infer that Shylock was obligated to follow through and convert to Christianity and to forsake Jewish ritual and synagogue to avoid a recanted judgement.