It is a very general question and a very general answer would be 'no'.
You may already know this ( and it may seem ridiculous ) but you actually need planning permission to put an ensuite bathroom into a protected structure.
The local conservation officer will be, by definition, conservative, will resist change and will be inclined towards ‘no’.
A more correct answer would be that 'it depends'. Planning applications are judged on a case by case basis. The works permissible to a traditional cottage, will differ from those permissible to a Georgian redbrick, or to a Victorian villa and so on.
So it depends on the protected structure.
It depends on why the building is protected, what it is that is of special interest about the protected structure in the first place. If you know that you then assess whether the ensuite might impact in conservation terms on that special interest or character.
It depends on the impact of the ensuite, eg. do you effect original plasterwork, joinery do you need to cut joists to get the soil pipe out, where does the soil pipe go down the front, side rear façade, etc.
It depends on the condition of the property. If the property is in poor condition and you are proposing to repair it, restore it, that will be taken into account and the ensuite might be seen as reasonable in that context.
It depends on other works that may have been carried out previously. If there were works carried out previously that were insensitive to the building, eg. bedsit kitchens, toilets, etc that you propose to remove, your ensuite would be judged in that context and you could reach a tipping point towards 'yes'.
It depends on what other works you are proposing. If there are other works proposed by you that along with the ensuite, which collectively might negatively impact ( in conservation terms ) on the property, then you could reach a tipping point towards 'no'.
So there you go, we hope that is helpful: a long answer to a short question: Good luck with your project.