I'm not entirely sure I understand your question (my bad) but I'll try to shed some light on what you can/can't do with QlikView Server and the QlikView Publisher.
Every QlikView installation is composed of a set of interdependent services. Although they are able to run separately, they need to communicate with each other to make things happen. A single QlikView server usually has 0 or 1 Publisher licenses. This does in no way mean that you have to install additional software when you enter a Publisher license. The software is already there, even if you have no Publisher license. It's just that without a P-license, the Publisher becomes a simple Reload engine with limited features. But the software is the same.
Whenever you install a Publisher license via the QMC, not only does it activate all advanced Publisher features, but it also allows you to move the Publisher service to a separate machine. That is especially useful when QlikView Service and Publisher service are fighting for resources, thereby bogging down the single machine on which they run. (Remember that the QlikView Service and Publisher have entirely different objectives.)
I'm not really sure whether this is simply impossible to do, but from a management and perfomance angle, I would never ever consider installing the same QlikView service on the same platform twice. It simply serves no purpose and will wreak havoc when loads start increasing. A QlikView Server with Publisher can do the same things, and way more than a QlikView Server without Publisher. So why would you consider running two QlikView Server solutions when you can simply host all of your doucments on a single installation that includes a Publisher?
Hope I made a few things clearer. If not, please tell us why you want to run two installations.
Yes you can serve two documents in a QlikView Server/Publisher setup. Whatever you configured for the "Old" app can be had in the new environment (I.e. with a Publisher) and you won't even need to change your "Old App" QVW or any of the underlying data files or data sources.
However, since the QlikView environment that includes a full Publisher offers way more features than one without, you will surely have to configure some additional settings (for example those relating to Distribution) to get the same reload strategy as before. Takes about 5 minutes or less.