I mean he could have been, in the same way that he could have secretly been a lizard man from the planet Klendagon.
Harold Bluetooth lived at a moment of transition for Scandinavia. There were the obvious religious influences of Christianity starting to permeate Scandinavia, but there were other changes in Danish society as well. The time of Harold's life saw the increased power of the Danish royal family, coming at the expense of regional warlords and powers. This increased political power is seen in the start of numerous large public works projects that were begun around this time, including large defensive fortifications in southern Denmark.
I bring this up because it is important to understand that Christianity was not an isolated interruption of Scandinavia life, but part of an ongoing process that integrated the far flung lands around the North Sea into a more cohesive political and cultural unit. Part of this newly introduced influence was Christianity, and it was moving relatively quickly throughout the area. There were Christian populations in Sweden, Norway, and Denmark already by the time of Harold's birth, and the new religion was only going from strength to strength. There were other changes coming about as well, new artistic patterns, methods of sailing, agriculture, and adornment were all coming about at this time. This is partly due to Scandinavia's increasing connection between itself, ie between Denmark and Norway, but also to other parts of Europe, namely Germany, England, and Frisia, that were exposing Scandinavia and the Norse people to increased amounts of trade and influence from Christianized Europe.
Once Harold came into power though there is some speculation that he strongly resisted the encroachment of Christian, and western European more broadly, influence. Part of this was the defensive fortifications that he erected in Southern Denmark, but he also seems to have engaged in a defensive paganism project as well. His father, Gorm the Old, was buried in a deliberately anachronistic style according to Anders Winroth. Harold deliberately evoked traditional pagan practices by interring his father in a massive, and very archaic, barrow as his resting place. Winroth posits that this was part of an effort on Harold's part to craft a more distinctive pagan identity to resist Christian influence. If this was his intention, it did not work. Harold himself converted to Christianity a few years later, dug up dear old dad, and buried him in the church in Jelling, presumably because his effort was not panning out particularly well.
It is worth dwelling on this point however. Winroth believes that the political situation of Scandinavia was primarily responsible for the conversion of the ruling class to Christianity, but we need to remember that this is not incompatible with personal belief as well. We do not need to necessarily assume that Harold was really a staunch pagan and merely caved to political pressures, or entered the Church purely as a cynical ploy to accrue more power and influence. Indeed, given the lengths that he went to, such as re-interring his father in a Church, patronizing churches around the country, converting the people, it is very likely that he held some Christian beliefs rather sincerely. Nor, does that diminish the very real practical benefits that Christianity brought him. Christianity also became tied with the increased power of the royal family. Patronage of ecclesiastical institutions and figures, church administration, and warm relations with the Papacy all contributed to the prestige and influence of the Danish royal family.