If it were to happen, would it have that negative an effect on how Barca operates?
Well, generally speaking, a membership corporation is congenial to a PLC, but the main difference is the influence of members of the former and shareholders of the latter.
The clubs' constitution, which would be superfluous after a transformation to a PLC, allows for member influence even on non-essential issues.
Shareholders on the other hand are limited to the rights the legal framework provides: Only decisions that concern the structure of the PLC itself require a resolution by the general meeting, such as but not limited to increase/decrease of capital stock, stock financing, merger, squeeze-out, you name it.
For example, looking at the Qatar Foundation/airways deal, abstracting away from how this was handled in practice, would not be up for debate in a PLC. Such matters are included in the managing boards power of representation.
Generally speaking, it would be a shift of power from the members/shareholders to the board of directors.
The actual issue though is that such a transformation could be a 'door opener' for a wide array of procedures. The PLC might be willing to acquire funding from outside investment groups, hedge funds or single investors via capital increase and issue of shares and before you realise you have all the people you don't want in the loop.
The PLC might decide to become listed on the stock exchange: Acquiring funding almost immediately comes at the downside of having an army of small shareholders with no correlation to the sport division whose rights are executed via banks due to their stock-authority and the only thing they are interested in (which can be observed at every general meeting ever) is that the PLC invests aka takes loans.
Add to that that sports are not really a stable and sustainable business but with a high degree of vicissitude, so the probability to attract locusts is high.
The pyramiding I mentioned earlier can be a way out of this dilemma, depending on how it is executed. But it might as well be that the EC rejects a procedure like this and tries to force a direct transformation in which case Barca should take the matter to the CJEU.
On the other hand, as Catorce mentioned, Barca would have to pay higher property and corporation taxes due to losing non-profit status which only 4 clubs were allowed to keep 20 odd years ago.