If your encryption algorithm is possible to decrypt and if the algorithm always produces the same number of bits of output as it has bits of input then clearly by the pigeon-hole principle every input sequence must map to exactly one output sequence. Therefore if the input is perfectly random the output will also be perfectly random.
This isn't always the case with practical implementations of encryption algorithms. Many produce outputs larger than their inputs due to padding, parameter specifications etc.
Also most "true random number generators" are not perfectly random. Encrypting the output will hide flaws in the underlying random number generator from statistical tests but that doesn't mean those flaws no longer exist, only that they can't be found without decrypting the output.
Always remember that statistical tests can only look for particular types of pattern, they cannot prove that a sequence is truely random.