I do not think there is anything that prohibits you from doing it on a web server. In fact I am sure there are others who have done it. It is not a built-in facility of the calibre web server, so offering this facility involves doing your own interfacing to the calibre command level tools.
However a word of caution - a conversion can take a long time. Minutes is not unusual, and hours have been known. This might mean that the mode of working you are envisaging could have problems.