The answer is that no-one knows - that's largely why quadratic programming is hard in practice.
A solver is such a chaotic system that it's no use even trying to predict how such modelling decisions will affect the outcome. Most of the time something works we don't really know why.
My advice is to never linearise yourself prematurely, as by doing so you are removing information from your model that the solver might be able to exploit. One exception to this rule is if your linearisation is not exact (e.g. you are outer approximating a continuous term). In this case, you are actually telling the solver that you are ok with sacrifising accuracy for that term, which can in turn improve performance. This is not a decision that the solver can make for you, so it needs to come from the modeller.
Generally speaking though, high performance solvers are advanced enough that linearising manually should only really be done as a very last resort. I generally advice users to first play around with solver settings before making any such changes to their models.
Note the "high performance" here - if you are using a less advanced solver, the situation is different and it becomes more likely that your linearisation might pay off.