No, the Imperial Cult died officially (as we see it today) with Diocletian. It started dying much earlier than that and was in reality revived under Decius, with more or less forced following under Decius and Diocletian. The very nature of the Imperial Cult makes it an impossibility during the Christianized empire, because in Christianity there is only one god, and having the emperor as a sort of pseudo-god at the side would be heresy (which is partly why the Christians refused to worship the emperor in the earlier empire).

You might speculate that the private cult lived on after Constantine came to power. Non-state-controlled religions are generally (seen throughout history) less obedient to sudden changes and it wouldn't be impossible for the private cult to keep on functioning in Roman homes. It is however just that, speculation, because the nature of private worship means that we don't have a lot of archaeological material left at all from it.