First of all, the Perlin method requires a random number generator as input. It seems deterministic in nature by itself. So if the random number repeats with a given seed, then I suppose it should always generate the same stream. In that case it is insecure as it is predictable even without any particular attack. Besides that, if the seed is a predetermined value then it could be considered a constant in the derived MT algorithm, and it would therefore go against the Kerckhoff principle.
As the Perlin method is not strictly made to be irreversible, I don't see how it would protect an insecure PRNG. For instance, I would expect that it generates certain maximum and minimum values for which the output of the random number generator can be established. If that happens for enough bits, then in the end enough state of the Mersenne Twister may be known to retrieve the seed, breaking any security present in the combination of the two algorithms.
Let's assume that the Perlin method at least leaks some information about the stream. In that case the question becomes: can you break the Mersenne Twister given enough output, even if that output is further apart? And that question I don't know the answer to; I would however not assume that it is impossible.
However, things will get worse: if the Mersenne Twister only uses a 32 bit seed and the Perlin method is indeed deterministic, then it is completely feasible to try all possible seed values and simply run the algorithms on them, comparing the output against known values. And as the 32 bit strength of the seed is nowhere near enough security, the algorithm would not just be theoretically but also practically broken as it would be easy to brute force the seed.
Practically this would require you to know the parameters of the specific Perlin noise generator as well, of course. Again, considering those secret would go against Kerckhoff's principle, so theoretically it would still not be secure even if those have enough strength to secure the implementation.