Through the injector?
I'd have thought the overflow valve would prevent that? It opens to outwards flow, not inwards.
Having recently helped repair a boiler with worn out safety-valve threads I'd certainly always use either a dedicated fitting on a pump plumbing, or the blow-down valve. The valve's short outlet pipe is usually sufficient for a push-fitted hose but there is no reason it could not be a screwed fitting to take a pump hose.
I have used this route without a pump, but a large funnel and short plastic tube. It was a bit slow but effective.
There is another problem with using the safety-valve bushes for filling, that if simply via a funnel any water escaping around the spout ends up inside the cladding.
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That boiler incidentally was given a "new" 2X hydraulic test as it had been modified.