The trouble with this question is that it's almost impossible give an absolute answer, although if pushed, I would say 'probably not.' The trouble is that we have no written sources from the Danelaw in the period, and the Anglo-Saxon sources we have aren't concerned with what would have been small-scale local level conversions.

There is some evidence that the opposite may have occurred: Although legend claims that King Edmund of East Anglia (St Edmund the Martyr) was tortured to death by the Vikings in 870 for refusing to renounce Christ, the Anglo-Saxon Chronicle states simply that he was killed in battle. Indeed, his 'martyr's death' bears resemblance to other Christian martyrology and may have been constructed as a propaganda tool. Either way, by the 890s, the Vikings in East Anglia were themselves propagating his cult, issuing coinage using Edmund's design and with the inscription SCE EADMVND REX or 'Saint Edmund the King'. Given that Guđrum's army is supposed to have converted following their defeat to Alfred at Edisbury, this may be a direct result, and illustrate that Edmund's martyrology had already gained sufficient credence that some Danes were seeking to atone for it.

In 909, Æthelred and Æthelflæd of Mercia lead an expedition to Bardney in Lincolnshire to capture the relics of St Oswald (originally a Mercian saint) and translate them to Gloucester. This may illustrate that the relics were still being venerated inside the Danelaw, and had not been looted or desecrated as might otherwise be expected.