Is the cabinet dustproof, and does fitting a brush insert make it dustproof?

No on both counts.

These are ventilated indoor data cabinets. They have airflow openings, panel joints, cable entries and a roof fan position, so they’re not sealed against dust.

A brush insert reduces the large open gap around the cables and gives the entry a neater finish, but air can still pass through it — and dust is quite capable of accompanying the air.

That becomes particularly relevant if you fit an extraction fan. You’ve not created a sealed clean-room cabinet with a brush strip; you’ve deliberately increased the movement of air through a ventilated enclosure.

Where dust accumulation matters, keep the surrounding environment reasonably clean and inspect the equipment periodically.