The union dispute won't have any impact on pay rises being approved, but the NEU guidance above only applies to maintained (LA) schools.
If you work for an academy, any pay rise has to be ratified by the trustees, as well as pay progression. If there's no money in the budget, the trustees may choose not to post a deficit budget, and will therefore not ratify the pay rises. This is rare- in the county I work in, all academy trusts stick to government published pay rises. But equally, schools are on the edge and if the money isn't there, it is a difficult decision for academies to make.
It's possible some academies will use impeding strike action as an excuse to delay pay rises, but this is disingenuous, to say the least.
The union campaign for fully funded pay rises succeeds, it actually makes it easier for academies to approve the pay rises, because my understanding is that academies and free schools aren't allowed to post repeated deficit budgets.
The NEU timescale looks like balloting after half term, which would realistically lead to a strike in January, due to the "cooling off" period mandated by legislation. I assume NASUWT are working to a similar time scale as co-ordinated strikes will be most effective.