Not really. The kind of Protestantism you're describing really only emerges as a major cultural force in the nineteenth century in the United States, and the large slice of the Christian pie it now claims is a result of, on the one hand, aggressive proselytising efforts by American churches among previously non-Protestant populations in Africa, Asia and South America, and on the other, by high rates of apostasy among Catholic, Orthodox and Mainline Protestant Churches. From a historical perspective, it's a novel and really quite bizarre phenomenon, enabled by the unique political and economic circumstances thrown up in the American West.
Protestantism secularism was not, for a very long time, what we recognise as secularism. It was about protecting the church from the state, rather than the state from the church, and it was still expected that the state would govern very much in line with religious principles and with the approval of religious authorities; Scotland was a virtual theocracy until the 1960s, despite the Kirk having been disestablished at its own request in the seventeenth century. This actually parallels certain strains of Islamic thought, which have tended to regard the state as something a bit grubby and disreputable and which should therefore be kept at arms length from the sanctity of the mosque and the madrasa, while still operating in accordance with the moral truths which those institutions propound.
Rather, modern secularism really emerges from the thought of French and English liberals, who lived in decidedly unsecular countries- England, to this day, has an established Protestant Church. We associate secularism with the Reformation largely because that was the mythology constructed by New England radicals during the American Revolution, who wanted to draw a line from their own secular revolution to their Congregationalist forebearers, and in doing so conflate the religious pluralism of the radical Reformation with their own modernising secularism.
