Sometimes, but not always. Shooting RAW gives you some room to correct underwater color, especially in clearer blue water and at shallower depths (around 60 feet / 18 m or less on a sunny day). In those conditions, you may be able to get acceptable results without a filter.

The problem is that underwater light loss is not just a simple white-balance issue: red light disappears quickly with depth. If there isn’t enough red information captured, pushing the RAW file to restore it can require such a large correction that other channels—especially blue—can become overexposed or the file can fall apart in quality.

So in many cases, post-processing alone won’t fully match using the correct filter. In green water or at greater depths, a filter becomes more important for ambient-light shooting.

That said, the best solution for strong color underwater is usually not a filter but an underwater strobe, which restores missing wavelengths rather than trying to recover them afterward.