There are a lot of unknowns with the SQE - no one has qualified via that route yet so it is really hard to comment on what would happen.
But just a few things to flag:
Your paralegal experience (whether in Corporate or in Disputes) may allow you to qualify where it is deemed to be QWE, but that doesn't mean that firms will consider it equivalent to a training contract seat. This is the major issue with the new qualification system. If we take it to its extreme, someone could use their work experience in a university free law clinic as QWE. That does not mean firms will necessarily value it as what they deem QWE to be. Therefore there is a risk that you become qualified but under-experienced, because you haven't worked at the level/complexity a trainee has.
The old qualification system created a need for seat rotations as trainees had to see three distinct areas of law. This meant someone sitting in something like corporate and then in litigation was common, as it allowed you to see different areas of law which was necessary to qualify. This requirement is no longer needed under the SQE. People could do the whole of the QWE in one practice area should the firm they are working for want that. This means the value of different experiences (seats/QWE) could change when looking to recruit NQs or junior qualified lawyers.
Although there is a lot of value in someone still seeing different areas of law (as
@FS has mentioned, there is value in that from a knowledge/skills perspective), what is unknown is whether we will start to see two types of "training contract" - one where you effectively specialise from the outset (some firms are doing this already) and one where you rotate around to work out where you want to qualify into. This change could have quite a big impact on NQ processes - although again, this is speculation as we won't really know the general trends of how it impacts qualification processes for a good 4-6+ years.
I am fairly sure though that if you qualified with only 2 years of experience in Corporate, it is going to be very difficult for you to become a disputes NQ as you won't have comparable experience to other NQs in the market who will have some disputes experience.