Yes it is. The Grand Duke has to give his written consent prior to marriage while the government does not. As the current constitution is very old and is reworked at the moment, it's entirely possible that this will change in the future. (The constitution currently delegates most matters to the house law.) What happens with those who either do not seek consent or marry without consent is laid down in the house law that was reworked during the last few years and re-published in 2012.
Of course Prince Charles' children are members of the Grand Ducal Family. The house law distinguishes between the Grand Ducal Line, Family and House.
For more about the matters of consent and who is part of the line, family and house, check this out: Luxarazzi : FAQ
Princess Sophie's male-line descendants are not in the line of succession which consists entirely of descendants of Grand Duchess Charlotte.