I am constructing our Accountability Chart with my team and I find it almost impossible not to consider the existing situation. Filling in the seats with names, but also the seats being (partially) defined by the positions that currently exist. Should we make two Accountability Charts, one with the current situation and one with the ideal situation?

Yes, it is helpful to build out a current state AC and a future state AC. 

It is important initially and periodically to define the seats without the names or even the existing positions in your organization. How would you design it if you were not constrained by what is? The key word is accountability - what are the outputs required for each seat to meet the business goal. Be clear first about what needs to be accomplished by your organization. Then work backwards to figure out the sub-outputs that get you those results. Divide and organize those sub-outputs into seats. Only then can you fill the seats with people that can produce those results for you. Now, in reality, those will likely be people that are already in seats, but if you are doing it right, there is usually going to be some turnover in the coming months once real accountability and expectations are clear.

This also often results in people being in multiple seats when you've defined the seats by function and outputs. That is OK - but in order to manage capacity, make sure you are clear with the employee about how much time is expected to be spent in each of their seats. 
That said, it is OK to put seats on the AC that are not yet filled - particularly ones that will be filled in the next 12-36 months. Defined them the same way and assume that the person in the seat above owns that seat until it is filled.